Introduction


To address the challenge of retaining talented employees, the leadership team of Frito Lay have engaged DDS Analytics to conduct an in-depth analysis aimed at uncovering the underlying factors behind employee turnover within their organization. This study, leveraging data from 870 employees across 36 distinct variables, is designed to yield actionable insights to inform decision-making processes. By employing a combination of visualizations, statistical methodologies, and the creation of predictive models, the objective is to provide strategic guidance and practical tools to enhance future strategies and organizational policies.

Presentation
View the video presentation of this analysis: https://youtu.be/aY4CYfuHOf4.

This imports necessary libraries. 

library(RCurl)
library(tidyverse)
library(ggplot2)
library(DataExplorer)
library(Hmisc) #rcorr(), generates a correlation matrix
library(corrplot) #to plot the correlation matrix
library(gridExtra) #to arrange plots in a grid
library(RColorBrewer)
library(caret) #ConfusionMatrix()
library(e1071) #naiveBayes()
library(class) #knn
library(combinat)
library(patchwork)
library(GGally)
library(kableExtra) #kable() tables
library(pander) #pander() tables
library(dplyr) #loading this after Hmisc because of conflict in summarize? can use summarise instead


Objective 1: Identify the top three factors that lead to attrition.


I import the primary data set from the cloud as cs2. Then, I convert the numerical variables that are Likert scale responses to factors, creating a new data frame, cs2_conv. 

# import data: CaseStudy2-data.csv from AWS S3 msdsds6306 bucket

cs2 = read.table(textConnection(getURL(
  "https://s3.us-east-2.amazonaws.com/msdsds6306/CaseStudy2-data.csv"
)), sep=",", header=TRUE, stringsAsFactors = TRUE)

# save a copy of the data
# write.csv(cs2, file = "data/CaseStudy2-data.csv", row.names = FALSE)

# get a sense of the data
str(cs2)
'data.frame':   870 obs. of  36 variables:
 $ ID                      : int  1 2 3 4 5 6 7 8 9 10 ...
 $ Age                     : int  32 40 35 32 24 27 41 37 34 34 ...
 $ Attrition               : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...
 $ BusinessTravel          : Factor w/ 3 levels "Non-Travel","Travel_Frequently",..: 3 3 2 3 2 2 3 3 3 2 ...
 $ DailyRate               : int  117 1308 200 801 567 294 1283 309 1333 653 ...
 $ Department              : Factor w/ 3 levels "Human Resources",..: 3 2 2 3 2 2 2 3 3 2 ...
 $ DistanceFromHome        : int  13 14 18 1 2 10 5 10 10 10 ...
 $ Education               : int  4 3 2 4 1 2 5 4 4 4 ...
 $ EducationField          : Factor w/ 6 levels "Human Resources",..: 2 4 2 3 6 2 4 2 2 6 ...
 $ EmployeeCount           : int  1 1 1 1 1 1 1 1 1 1 ...
 $ EmployeeNumber          : int  859 1128 1412 2016 1646 733 1448 1105 1055 1597 ...
 $ EnvironmentSatisfaction : int  2 3 3 3 1 4 2 4 3 4 ...
 $ Gender                  : Factor w/ 2 levels "Female","Male": 2 2 2 1 1 2 2 1 1 2 ...
 $ HourlyRate              : int  73 44 60 48 32 32 90 88 87 92 ...
 $ JobInvolvement          : int  3 2 3 3 3 3 4 2 3 2 ...
 $ JobLevel                : int  2 5 3 3 1 3 1 2 1 2 ...
 $ JobRole                 : Factor w/ 9 levels "Healthcare Representative",..: 8 6 5 8 7 5 7 8 9 1 ...
 $ JobSatisfaction         : int  4 3 4 4 4 1 3 4 3 3 ...
 $ MaritalStatus           : Factor w/ 3 levels "Divorced","Married",..: 1 3 3 2 3 1 2 1 2 2 ...
 $ MonthlyIncome           : int  4403 19626 9362 10422 3760 8793 2127 6694 2220 5063 ...
 $ MonthlyRate             : int  9250 17544 19944 24032 17218 4809 5561 24223 18410 15332 ...
 $ NumCompaniesWorked      : int  2 1 2 1 1 1 2 2 1 1 ...
 $ Over18                  : Factor w/ 1 level "Y": 1 1 1 1 1 1 1 1 1 1 ...
 $ OverTime                : Factor w/ 2 levels "No","Yes": 1 1 1 1 2 1 2 2 2 1 ...
 $ PercentSalaryHike       : int  11 14 11 19 13 21 12 14 19 14 ...
 $ PerformanceRating       : int  3 3 3 3 3 4 3 3 3 3 ...
 $ RelationshipSatisfaction: int  3 1 3 3 3 3 1 3 4 2 ...
 $ StandardHours           : int  80 80 80 80 80 80 80 80 80 80 ...
 $ StockOptionLevel        : int  1 0 0 2 0 2 0 3 1 1 ...
 $ TotalWorkingYears       : int  8 21 10 14 6 9 7 8 1 8 ...
 $ TrainingTimesLastYear   : int  3 2 2 3 2 4 5 5 2 3 ...
 $ WorkLifeBalance         : int  2 4 3 3 3 2 2 3 3 2 ...
 $ YearsAtCompany          : int  5 20 2 14 6 9 4 1 1 8 ...
 $ YearsInCurrentRole      : int  2 7 2 10 3 7 2 0 1 2 ...
 $ YearsSinceLastPromotion : int  0 4 2 5 1 1 0 0 0 7 ...
 $ YearsWithCurrManager    : int  3 9 2 7 3 7 3 0 0 7 ...
df_summary = summary(cs2)
df_summary
       ID             Age        Attrition           BusinessTravel
 Min.   :  1.0   Min.   :18.00   No :730   Non-Travel       : 94   
 1st Qu.:218.2   1st Qu.:30.00   Yes:140   Travel_Frequently:158   
 Median :435.5   Median :35.00             Travel_Rarely    :618   
 Mean   :435.5   Mean   :36.83                                     
 3rd Qu.:652.8   3rd Qu.:43.00                                     
 Max.   :870.0   Max.   :60.00                                     
                                                                   
   DailyRate                       Department  DistanceFromHome   Education    
 Min.   : 103.0   Human Resources       : 35   Min.   : 1.000   Min.   :1.000  
 1st Qu.: 472.5   Research & Development:562   1st Qu.: 2.000   1st Qu.:2.000  
 Median : 817.5   Sales                 :273   Median : 7.000   Median :3.000  
 Mean   : 815.2                                Mean   : 9.339   Mean   :2.901  
 3rd Qu.:1165.8                                3rd Qu.:14.000   3rd Qu.:4.000  
 Max.   :1499.0                                Max.   :29.000   Max.   :5.000  
                                                                               
          EducationField EmployeeCount EmployeeNumber   EnvironmentSatisfaction
 Human Resources : 15    Min.   :1     Min.   :   1.0   Min.   :1.000          
 Life Sciences   :358    1st Qu.:1     1st Qu.: 477.2   1st Qu.:2.000          
 Marketing       :100    Median :1     Median :1039.0   Median :3.000          
 Medical         :270    Mean   :1     Mean   :1029.8   Mean   :2.701          
 Other           : 52    3rd Qu.:1     3rd Qu.:1561.5   3rd Qu.:4.000          
 Technical Degree: 75    Max.   :1     Max.   :2064.0   Max.   :4.000          
                                                                               
    Gender      HourlyRate     JobInvolvement     JobLevel    
 Female:354   Min.   : 30.00   Min.   :1.000   Min.   :1.000  
 Male  :516   1st Qu.: 48.00   1st Qu.:2.000   1st Qu.:1.000  
              Median : 66.00   Median :3.000   Median :2.000  
              Mean   : 65.61   Mean   :2.723   Mean   :2.039  
              3rd Qu.: 83.00   3rd Qu.:3.000   3rd Qu.:3.000  
              Max.   :100.00   Max.   :4.000   Max.   :5.000  
                                                              
                      JobRole    JobSatisfaction  MaritalStatus MonthlyIncome  
 Sales Executive          :200   Min.   :1.000   Divorced:191   Min.   : 1081  
 Research Scientist       :172   1st Qu.:2.000   Married :410   1st Qu.: 2840  
 Laboratory Technician    :153   Median :3.000   Single  :269   Median : 4946  
 Manufacturing Director   : 87   Mean   :2.709                  Mean   : 6390  
 Healthcare Representative: 76   3rd Qu.:4.000                  3rd Qu.: 8182  
 Sales Representative     : 53   Max.   :4.000                  Max.   :19999  
 (Other)                  :129                                                 
  MonthlyRate    NumCompaniesWorked Over18  OverTime  PercentSalaryHike
 Min.   : 2094   Min.   :0.000      Y:870   No :618   Min.   :11.0     
 1st Qu.: 8092   1st Qu.:1.000              Yes:252   1st Qu.:12.0     
 Median :14074   Median :2.000                        Median :14.0     
 Mean   :14326   Mean   :2.728                        Mean   :15.2     
 3rd Qu.:20456   3rd Qu.:4.000                        3rd Qu.:18.0     
 Max.   :26997   Max.   :9.000                        Max.   :25.0     
                                                                       
 PerformanceRating RelationshipSatisfaction StandardHours StockOptionLevel
 Min.   :3.000     Min.   :1.000            Min.   :80    Min.   :0.0000  
 1st Qu.:3.000     1st Qu.:2.000            1st Qu.:80    1st Qu.:0.0000  
 Median :3.000     Median :3.000            Median :80    Median :1.0000  
 Mean   :3.152     Mean   :2.707            Mean   :80    Mean   :0.7839  
 3rd Qu.:3.000     3rd Qu.:4.000            3rd Qu.:80    3rd Qu.:1.0000  
 Max.   :4.000     Max.   :4.000            Max.   :80    Max.   :3.0000  
                                                                          
 TotalWorkingYears TrainingTimesLastYear WorkLifeBalance YearsAtCompany  
 Min.   : 0.00     Min.   :0.000         Min.   :1.000   Min.   : 0.000  
 1st Qu.: 6.00     1st Qu.:2.000         1st Qu.:2.000   1st Qu.: 3.000  
 Median :10.00     Median :3.000         Median :3.000   Median : 5.000  
 Mean   :11.05     Mean   :2.832         Mean   :2.782   Mean   : 6.962  
 3rd Qu.:15.00     3rd Qu.:3.000         3rd Qu.:3.000   3rd Qu.:10.000  
 Max.   :40.00     Max.   :6.000         Max.   :4.000   Max.   :40.000  
                                                                         
 YearsInCurrentRole YearsSinceLastPromotion YearsWithCurrManager
 Min.   : 0.000     Min.   : 0.000          Min.   : 0.00       
 1st Qu.: 2.000     1st Qu.: 0.000          1st Qu.: 2.00       
 Median : 3.000     Median : 1.000          Median : 3.00       
 Mean   : 4.205     Mean   : 2.169          Mean   : 4.14       
 3rd Qu.: 7.000     3rd Qu.: 3.000          3rd Qu.: 7.00       
 Max.   :18.000     Max.   :15.000          Max.   :17.00       
                                                                
# convert numerical ranking variables to factors
numVars_to_fact = c("Education", "EnvironmentSatisfaction",
                    "JobInvolvement", "JobLevel", "JobSatisfaction",
                    "PerformanceRating", "RelationshipSatisfaction",
                    "StockOptionLevel", "WorkLifeBalance")
cs2_conv = cs2 %>%
  mutate(across(all_of(numVars_to_fact), as.factor))
# check the conversion
# str(cs2_conv)

# get the proportion of attrition
summary(cs2_conv$Attrition)
 No Yes 
730 140 
NoAttProb = summary(cs2_conv$Attrition)["No"] / sum(summary(cs2_conv$Attrition))
NoAttProb
       No 
0.8390805 
AttProb = summary(cs2_conv$Attrition)["Yes"] / sum(summary(cs2_conv$Attrition))
AttProb
      Yes 
0.1609195



For the exploratory data analysis (EDA), first I visualize the data. I loop through and plot nearly all the numerical variables in histograms and frequency polygons by density grouped by attrition category. I also loop through each categorical variable, find the proportion of each level within each attrition category and plot them as bar charts. 

# plot the distributions of numerical variables with respect to attrition group

# select all variables except ID, EmployeeCount (all=1), and StandardHours (all=80))
cs2_conv_subset = cs2_conv %>% select(-ID, -EmployeeCount, -StandardHours)
# check the modification
# str(cs2_conv_subset)

# filter the numerical variables
numVars = sapply(cs2_conv_subset, is.numeric)
cs2_numerical = cs2_conv_subset[, numVars] #this does not include integers that were converted to factors
# check the result
# str(cs2_numerical)

# function to calculate binwidth (by Freedman-Diaconis rule, Bin Width=2*IQR/(cuberoot(n)))
# and flexibly set a binwidth for each variable
calculate_binwidth = function(data) {
  IQR = quantile(data, 0.75) - quantile(data, 0.25)
  n = length(data)
  bw = 2 * IQR / (n^(1/3))
  return(bw)
}

# iterate over numerical variables and create plots
dist_plots = list()
for (col in names(cs2_numerical)) {
  # calculate binwidth for current variable
  bw = calculate_binwidth(cs2_conv[[col]])
  
  # create a histogram with density not frequency for each variable
  hist_plot = cs2_conv %>%
    ggplot(aes(x = .data[[col]], y = after_stat(density), fill = Attrition)) +
    geom_histogram(binwidth = bw) +
    facet_wrap(~Attrition)
    labs(title = paste("Histogram of", col))

  # save the histogram plot
  # ggsave(filename = paste0("plots/EDA/", col, "_histogram.png"), plot = hist_plot, device = "png")
  
  # create a frequency polygon plot for each variable
  freqpoly_plot = cs2_conv %>%
    ggplot(aes(x = .data[[col]], y = after_stat(density), color = Attrition)) +
    geom_freqpoly(binwidth = bw) +
    labs(title = paste("Frequency Polygon of", col))
  
  # save the frequency polygon plot
  # ggsave(filename = paste0("plots/EDA/", col, "_freqpoly.png"), plot = freqpoly_plot, device = "png")

  dist_plots[[col]] = list(hist_plot, freqpoly_plot)
}

# display plots
for (col in names(cs2_numerical)) {
  print(dist_plots[[col]][[1]]) #displays histogram
  print(dist_plots[[col]][[2]]) #displays frequency polygon
}

# make bar charts to visualize categorical variables with respect to attrition group
# filter categorical variables (factors)
cs2_categorical = cs2_conv %>%
  select(where(is.factor) & -Over18) #Over18(all=Y)
# check the result
# str(cs2_categorical)

# iterate over categorical variables and create bar plots
bar_plots = list()
for (col in names(cs2_categorical)) {
  if (col != "Attrition") { #check if the column is not "Attrition"
    # calculate proportions of each category within each level of Attrition
    prop_cat_data = cs2_categorical %>%
      group_by(Attrition = cs2_conv$Attrition, .data[[col]]) %>%
      dplyr::summarize(count = n(), .groups = "drop") %>% #this gets rid of the warning message about grouping
      group_by(Attrition) %>%
      mutate(proportion = count / sum(count))
    
    bar_plot = prop_cat_data %>%
      ggplot(aes(x = .data[[col]], y = proportion, fill = Attrition)) +
      geom_bar(position = "dodge", stat = "identity") +
      labs(title = paste("Bar Chart of", col)) + 
      coord_flip()
    
    # save the bar plot
    # ggsave(filename = paste0("plots/EDA/", col, "_barplot.png"), plot = bar_plot, device = "png")
    
    bar_plots[[col]] = bar_plot
  }
}

# display plots if they exist (there is no plot for attrition)
for (col in names(cs2_categorical)) {
  if (!is.null(bar_plots[[col]]))
    print(bar_plots[[col]])
}



Many of the numerical features have right-skewed distributions, e.g. salary, and the variables that are related to years working.

With the plots above, I look for features that may have higher attrition.

Numerical features with higher attrition may include the following.

Categorical features with higher attrition may include the following.

Something odd, performance rating doesn’t seem to have much effect, but attrition is higher in 4.

These factors could be correlated with age and higher skill: age, education, environmental satisfaction(?), job involvement(?), job level, job satisfaction(?), marital status, monthly income, overtime, stock option level, total working years, years at company, years in current role, years with current manager.


The next step of my EDA is to check for missing values before proceeding with further analysis. 

# are there missing values
missing_count = sum(is.na(cs2_conv) | cs2_conv == "")
writeLines(sprintf("There are %d missing values in the dataset.", missing_count))
There are 0 missing values in the dataset.


The data set appears to be complete.


This function generates a report to facilitate EDA. It is good to know about and look over for ideas, though perhaps not as useful as my step-by-step analysis. 

create_report(cs2_conv, y = "Attrition")



For the numerical variables, I generate a matrix of correlation coefficients and plot them. There is also a function to generate a table of correlation and p-values, but only the first few rows are displayed for the sake of space. I find the matrix to be sufficient. 


# compute correlation matrix and p-values
cor_mat = rcorr(as.matrix(cs2_numerical))

# This function makes a table of each variable combination with the correlation coefficient and p-value
# ++++++++++++++++++++++++++++
# flattenCorrMatrix
# ++++++++++++++++++++++++++++
# cormat : matrix of the correlation coefficients
# pmat : matrix of the correlation p-values
flattenCorrMatrix = function(cormat, pmat) {
  ut <- upper.tri(cormat)
  data.frame(
    row = rownames(cormat)[row(cormat)[ut]],
    column = rownames(cormat)[col(cormat)[ut]],
    cor  =(cormat)[ut],
    p = pmat[ut]
    )
}

# call the function with extracted correlation and p-values
corrTable = flattenCorrMatrix(cor_mat$r, cor_mat$P)
kable(head(corrTable), caption = "correlation coefficients") %>% kable_styling(full_width = FALSE, position = "left")
correlation coefficients
row column cor p
Age DailyRate 0.0127367 0.7075463
Age DistanceFromHome 0.0066471 0.8447809
DailyRate DistanceFromHome 0.0149445 0.6597985
Age EmployeeNumber 0.0104706 0.7577761
DailyRate EmployeeNumber -0.0297344 0.3810454
DistanceFromHome EmployeeNumber -0.0046415 0.8912620 

# plot the correlations using corrplot
corrplot(cor_mat$r, type = "upper", order = "hclust", insig = "blank")

# If I include the p.mat argument I get an error.
# I think because pairs of the same variable create an NA.


From this matrix, there is evidence of correlation between some numerical variables, including total working years with these below:

Next in the EDA, I look at each numerical variable for statistically significant evidence that the mean value of that variable differs between the populations of employees that stay or go. I perform t-tests for each numerical feature with the null hypothesis that the means of the attrition groups are equal. 

# extract numerical column names from cs2_numerical
numerical_columns = colnames(cs2_numerical)

# initialize an empty list to store t-test results
t_test_results = list()

# initialize an empty dataframe to store summary statistics
summary_table = data.frame(variable = character(), 
                            mean_Attrition_Yes = numeric(), 
                            mean_Attrition_No = numeric(),
                            p_value = numeric(),
                            stringsAsFactors = FALSE)

# initialize empty lists to store variable names with p-value < 0.05 or < 0.001
significant_variables = list() #p-value < 0.05
super_sig_variables = list() # p-value < 0.001

# loop through each numerical variable
for (col in numerical_columns) {
  # get data for the current column
  data_col = cs2_conv[[col]]
    
  # run a t-test
  t_test_result = t.test(data_col ~ Attrition, data = cs2_conv)
      
  # store t-test result in the list
  t_test_results[[col]] = t_test_result
      
  # extract relevant information and add to summary table
  summary_table = summary_table %>%
    add_row(variable = col,
      mean_Attrition_Yes = mean(data_col[cs2_conv$Attrition == "Yes"], na.rm = TRUE),
      mean_Attrition_No = mean(data_col[cs2_conv$Attrition == "No"], na.rm = TRUE),
      p_value = t_test_result$p.value)
      
  # check if p-value is less than 0.05
  if (t_test_result$p.value < 0.05) {
  significant_variables[[col]] = t_test_result
  }
  # check if p-value is less than 0.001
  if (t_test_result$p.value < 0.001) {
  super_sig_variables[[col]] = t_test_result
  }
}

# print summary table
kable(summary_table, caption = "t-test results") %>% kable_styling(full_width = FALSE, position = "left")
t-test results
variable mean_Attrition_Yes mean_Attrition_No p_value
Age 33.785714 37.412329 0.0000505
DailyRate 784.292857 821.160274 0.3188749
DistanceFromHome 10.957143 9.028767 0.0164052
EmployeeNumber 998.371429 1035.865753 0.4978776
HourlyRate 67.292857 65.291781 0.2744798
MonthlyIncome 4764.785714 6702.000000 0.0000002
MonthlyRate 13624.285714 14460.123288 0.1980950
NumCompaniesWorked 3.078571 2.660274 0.0978823
PercentSalaryHike 15.328571 15.175342 0.6692297
TotalWorkingYears 8.185714 11.602740 0.0000007
TrainingTimesLastYear 2.650000 2.867123 0.0594832
YearsAtCompany 5.192857 7.301370 0.0002563
YearsInCurrentRole 2.907143 4.453425 0.0000015
YearsSinceLastPromotion 2.135714 2.175343 0.8983165
YearsWithCurrManager 2.942857 4.369863 0.0000051 
# print list of variables with p-value < 0.05
significant_variable_names = names(significant_variables)
cat("\nVariables with p-value < 0.05:\n", paste(significant_variable_names, collapse = ", "))

Variables with p-value < 0.05:
 Age, DistanceFromHome, MonthlyIncome, TotalWorkingYears, YearsAtCompany, YearsInCurrentRole, YearsWithCurrManager
# print list of variables with p-value < 0.001
super_sig_variable_names = names(super_sig_variables)
cat("\nVariables with p-value < 0.001:\n", paste(super_sig_variable_names, collapse = ", "))

Variables with p-value < 0.001:
 Age, MonthlyIncome, TotalWorkingYears, YearsAtCompany, YearsInCurrentRole, YearsWithCurrManager
# print full t-test results for variables with p-value < 0.001
cat("\nT-test results for variables with p-value < 0.001:\n")

T-test results for variables with p-value < 0.001:
for (col in super_sig_variable_names) {
  cat("Variable:", col, "\n")
  print(super_sig_variables[[col]])
  cat("\n")
}
Variable: Age 

    Welch Two Sample t-test

data:  data_col by Attrition
t = 4.1509, df = 184.91, p-value = 5.05e-05
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
 1.902905 5.350324
sample estimates:
 mean in group No mean in group Yes 
         37.41233          33.78571 


Variable: MonthlyIncome 

    Welch Two Sample t-test

data:  data_col by Attrition
t = 5.3249, df = 228.45, p-value = 2.412e-07
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
 1220.382 2654.047
sample estimates:
 mean in group No mean in group Yes 
         6702.000          4764.786 


Variable: TotalWorkingYears 

    Welch Two Sample t-test

data:  data_col by Attrition
t = 5.1364, df = 201.19, p-value = 6.596e-07
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
 2.105259 4.728792
sample estimates:
 mean in group No mean in group Yes 
        11.602740          8.185714 


Variable: YearsAtCompany 

    Welch Two Sample t-test

data:  data_col by Attrition
t = 3.7256, df = 191.55, p-value = 0.0002563
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
 0.9922099 3.2248155
sample estimates:
 mean in group No mean in group Yes 
         7.301370          5.192857 


Variable: YearsInCurrentRole 

    Welch Two Sample t-test

data:  data_col by Attrition
t = 4.9513, df = 208, p-value = 1.522e-06
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
 0.9306052 2.1619584
sample estimates:
 mean in group No mean in group Yes 
         4.453425          2.907143 


Variable: YearsWithCurrManager 

    Welch Two Sample t-test

data:  data_col by Attrition
t = 4.6826, df = 209.75, p-value = 5.084e-06
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
 0.8262439 2.0277679
sample estimates:
 mean in group No mean in group Yes 
         4.369863          2.942857


This provides additional evidence of numerical variables that likely influence attrition to narrow the pool of important features in the data set.

Variables with p-value < 0.05: Age, DistanceFromHome, MonthlyIncome, TotalWorkingYears, YearsAtCompany, YearsInCurrentRole, YearsWithCurrManager
(The last 5 are highly correlated as I saw above.)

Variables with p-value < 0.001: Age, MonthlyIncome, TotalWorkingYears, YearsAtCompany, YearsInCurrentRole, YearsWithCurrManager


To gather statistical evidence of categorical variables associated with attrition, I perform chi-square tests for each categorical feature with the null hypothesis that the proportion of attrition is the same across all categories (feature levels). 

# extract categorical column names from cs2_categorical, excluding Attrition
categorical_columns = colnames(cs2_categorical)
categorical_columns = categorical_columns[categorical_columns != "Attrition"]

# initialize an empty list to store chi-square test results
chisq_test_results = list()

# initialize an empty dataframe to store summary statistics
summary_table2 = data.frame(variable = character(), 
                            p_value = numeric(),
                            stringsAsFactors = FALSE)

# initialize empty lists to store variable names with p-value < 0.05 or < 0.001
significant_variables2 = list()
super_sig_variables2 = list()

# loop through each categorical variable
for (col in categorical_columns) {
  # create a contingency table for the chi-square test
  contingency_table = table(cs2_conv[[col]], cs2_conv$Attrition)
  # print(contingency_table)
  
  # run a chi-square test
  chisq_test_result = chisq.test(contingency_table)
      
  # store chi-square test result in the list
  chisq_test_results[[col]] = chisq_test_result
      
  # extract relevant information and add to summary table
  summary_table2 = summary_table2 %>%
    add_row(variable = col,
      p_value = chisq_test_result$p.value)
      
  # check if p-value is less than 0.05
  if (chisq_test_result$p.value < 0.05) {
  significant_variables2[[col]] = chisq_test_result
  }
  # check if p-value is less than 0.001
  if (chisq_test_result$p.value < 0.001) {
  super_sig_variables2[[col]] = chisq_test_result
  }
}

# print summary table
kable(summary_table2, caption = "chi-square test results") %>% kable_styling(full_width = FALSE, position = "left")
chi-square test results
variable p_value
BusinessTravel 0.0499254
Department 0.0094238
Education 0.6242838
EducationField 0.2682198
EnvironmentSatisfaction 0.0105409
Gender 0.5151297
JobInvolvement 0.0000000
JobLevel 0.0000000
JobRole 0.0000000
JobSatisfaction 0.0111512
MaritalStatus 0.0000000
OverTime 0.0000000
PerformanceRating 0.7461706
RelationshipSatisfaction 0.3727117
StockOptionLevel 0.0000000
WorkLifeBalance 0.0024951 
# print list of variables with p-value < 0.05
significant_variable_names2 = names(significant_variables2)
cat("\nVariables with p-value < 0.05:\n", paste(significant_variable_names2, collapse = ", "))

Variables with p-value < 0.05:
 BusinessTravel, Department, EnvironmentSatisfaction, JobInvolvement, JobLevel, JobRole, JobSatisfaction, MaritalStatus, OverTime, StockOptionLevel, WorkLifeBalance
# print list of variables with p-value < 0.001
super_sig_variable_names2 = names(super_sig_variables2)
cat("\nVariables with p-value < 0.001:\n", paste(super_sig_variable_names2, collapse = ", "))

Variables with p-value < 0.001:
 JobInvolvement, JobLevel, JobRole, MaritalStatus, OverTime, StockOptionLevel
# print full chi-square test results for variables with p-value < 0.001
cat("\nChi-square test results for variables with p-value < 0.001:\n")

Chi-square test results for variables with p-value < 0.001:
for (col in super_sig_variable_names2) {
  cat("Variable:", col, "\n")
  print(super_sig_variables2[[col]])
  cat("\n")
}
Variable: JobInvolvement 

    Pearson's Chi-squared test

data:  contingency_table
X-squared = 41.465, df = 3, p-value = 5.211e-09


Variable: JobLevel 

    Pearson's Chi-squared test

data:  contingency_table
X-squared = 41.533, df = 4, p-value = 2.085e-08


Variable: JobRole 

    Pearson's Chi-squared test

data:  contingency_table
X-squared = 60.543, df = 8, p-value = 3.647e-10


Variable: MaritalStatus 

    Pearson's Chi-squared test

data:  contingency_table
X-squared = 34.406, df = 2, p-value = 3.379e-08


Variable: OverTime 

    Pearson's Chi-squared test with Yates' continuity correction

data:  contingency_table
X-squared = 62.762, df = 1, p-value = 2.333e-15


Variable: StockOptionLevel 

    Pearson's Chi-squared test

data:  contingency_table
X-squared = 56.245, df = 3, p-value = 3.724e-12


Although, the assumptions of a chi-square test may be violated here, a deeper knowledge of the test would be helpful, and use of alternative tests might be more appropriate, this at least provides additional evidence of categorical variables that likely influence attrition, facilitating a narrower pool of variables to consider.

Variables with p-value < 0.05: BusinessTravel, Department, EnvironmentSatisfaction, JobInvolvement, JobLevel, JobRole, JobSatisfaction, MaritalStatus, OverTime, StockOptionLevel, WorkLifeBalance

Variables with p-value < 0.001: JobInvolvement, JobLevel, JobRole, MaritalStatus, OverTime, StockOptionLevel


To look at co-variation among numerical variables that seem likely to influence attrition, I make scatter plots of all combinations of those with highly significant t-test results. 

# look at co-variation among numerical variables

# function to create scatter plots for each pair of variables
make_scatterplot = function(var1, var2) {
  cs2_conv %>% 
    ggplot(aes(x = .data[[var1]], y = .data[[var2]], color = Attrition)) +
    geom_point(alpha = 0.5, position = "jitter") +
    geom_smooth() +
    labs(title = paste(var1, "vs", var2))
}

# loop through each variable
for (i in 1:(length(super_sig_variable_names) - 1)) {
  var1 = super_sig_variable_names[i]
  
  # plot var1 with every other variable that comes after it in the list
  for (j in (i + 1):length(super_sig_variable_names)) {
    var2 = super_sig_variable_names[j]
    scatter = make_scatterplot(var1, var2)
    
    # display and save the individual plots
    print(scatter) # using print() so it's easier to find where I call the plot
    filename = paste0("plots/EDA/scatter_", var1, "_vs_", var2, ".png")
    # ggsave(filename, plot = scatter, device = "png")
  }
}



To do the same for combinations of numerical and categorical variables, I make boxplots of all combinations of those with highly significant t-test and chi-square test results. 

# look at co-variation between numerical and categorical variables

# function to create boxplots for each pair of variables
make_boxplot = function(catvar, numvar) {
  cs2_conv %>% group_by(Attrition) %>% 
    ggplot(aes(x = .data[[catvar]], y = .data[[numvar]], fill = Attrition)) +
    geom_boxplot() +
    coord_flip() +
    labs(title = paste(catvar, "vs", numvar))
}

# loop through each variable
for (i in 1:(length(super_sig_variable_names2))) {
  catvar = super_sig_variable_names2[i]
  
  # plot catvar with every numvar
  for (j in 1:length(super_sig_variable_names)) {
    numvar = super_sig_variable_names[j]
    boxplt = make_boxplot(catvar, numvar)
    
    # display and save the individual plots
    # I tried to display them in a grid in the interest of space, but they are just too small.
    print(boxplt)
    filename = paste0("plots/EDA/boxplt_", catvar, "_vs_", numvar, ".png")
    # ggsave(filename, plot = boxplt, device = "png")
  }
}



To do the same for combinations of categorical variables, I make bar charts of all combinations of those with highly significant chi-square test results. 

# look at co-variation among categorical variables

# It probably is easier to see relationships if I were to calculate proportions a different way to normalize the data.
# Currently, proportions are calculated like this. For each attrition group, and each level of variable 1, the count of each level of variable 2 (the fill variable) is divided by the sum of the total count for all levels of that variable (within the attrition and variable 1 level).

make_barchart = function(var1, var2) {
  cs2_conv %>% 
    group_by(Attrition, .data[[var1]], .data[[var2]]) %>%
    dplyr::summarize(n = n(), .groups = 'drop') %>%  #count occurrences within each group
    group_by(Attrition, .data[[var1]]) %>%  # group by Attrition and var1
    mutate(prop = n / sum(n)) %>% #calculate proportion within each group
    ggplot(aes(y = .data[[var1]], x = prop, fill = .data[[var2]])) +  #use prop as fill
    geom_bar(stat = "identity", position = position_dodge2(preserve = "single")) +
    facet_wrap(~Attrition, labeller = labeller(Attrition = c("No" = "No Attrition", "Yes" = "Yes Attrition"))) +
    labs(title = paste(var1, "vs", var2),
         y = var1,
         x = paste0("Proportion of ", var2, " within Attrition and ", var1, " level"),
         fill = var2) +
    theme_bw() +
    theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
    scale_fill_brewer(palette = "Set1")
}

# loop through each variable
for (i in 1:(length(super_sig_variable_names2) - 1)) {
  var1 = super_sig_variable_names2[i]
    
  for (j in (i + 1):length(super_sig_variable_names2)) {
    var2 = super_sig_variable_names2[j]
    barplt = make_barchart(var1, var2)
    
    # display and save the individual plots
    print(barplt)
    filename = paste0("plots/EDA/barplt_", var1, "_vs_", var2, ".png")
    # ggsave(filename, plot = barplt, device = "png")
  }
}



Observations from co-variation plots

Job level

Marital Status

Overtime and Stock Option

Monthly income

Some additional ideas:

As there is high correlation between total working years, years at company, years in current role and years with current manager, I want to see if deriving one variable from two of these, might help offset the correlation with age and extract possibly more meaningful information with the use of fewer variables. 

cs2_conv2 = cs2_conv %>% 
  mutate(
    PercentWrkYrsAtCompany = ifelse(TotalWorkingYears == 0, 0,
                                    round(YearsAtCompany / TotalWorkingYears * 100, 2)),
    PercentYrs_wManager = ifelse(TotalWorkingYears == 0, 0,
                                 round(YearsWithCurrManager / TotalWorkingYears * 100, 2)),
    PercentYrs_inRole = ifelse(TotalWorkingYears == 0, 0,
                               round(YearsInCurrentRole / TotalWorkingYears * 100, 2)),
    PercentYrs_inRoleAtComp = ifelse(YearsAtCompany == 0, 0,
                               round(YearsInCurrentRole / YearsAtCompany * 100, 2))
  )
# str(cs2_conv2)
# summary(cs2_conv2)

# plot these derived variables with other variables that seem relevant and alone to see the distributions
cs2_conv2 %>% ggplot(aes(x = Age, y = PercentWrkYrsAtCompany, color = Attrition)) +
  geom_point(alpha = 0.5, position = "jitter") + geom_smooth()

cs2_conv2 %>% ggplot(aes(x = MonthlyIncome, y = PercentWrkYrsAtCompany, color = Attrition)) +
  geom_point(alpha = 0.5, position = "jitter") + geom_smooth()

cs2_conv2 %>% ggplot(aes(x = Age, y = PercentYrs_inRoleAtComp, color = Attrition)) +
  geom_point(alpha = 0.5, position = "jitter") + geom_smooth()

cs2_conv2 %>% ggplot(aes(x = MonthlyIncome, y = PercentYrs_inRoleAtComp, color = Attrition)) +
  geom_point(alpha = 0.5, position = "jitter") + geom_smooth()

cs2_conv2 %>% ggplot(aes(x = MaritalStatus, y = PercentWrkYrsAtCompany, fill = Attrition)) +
  geom_boxplot(position = "dodge")

cs2_conv2 %>% ggplot(aes(x = JobLevel, y = PercentWrkYrsAtCompany, fill = Attrition)) +
  geom_boxplot(position = "dodge")

cs2_conv2 %>% ggplot(aes(x = MaritalStatus, y = PercentYrs_inRoleAtComp, fill = Attrition)) +
  geom_boxplot(position = "dodge")

cs2_conv2 %>% ggplot(aes(x = JobLevel, y = PercentYrs_inRoleAtComp, fill = Attrition)) +
  geom_boxplot(position = "dodge")

cs2_conv2 %>% ggplot(aes(x = PercentWrkYrsAtCompany, after_stat(density), fill = Attrition)) +
  geom_histogram(binwidth = 10) + facet_wrap(~Attrition)

cs2_conv2 %>% ggplot(aes(x = PercentYrs_inRoleAtComp, y = after_stat(density), fill = Attrition)) +
  geom_histogram(binwidth = 10) + facet_wrap(~Attrition)

# run t-tests to check for possible differences
t.test(PercentWrkYrsAtCompany ~ Attrition, data = cs2_conv2)

    Welch Two Sample t-test

data:  PercentWrkYrsAtCompany by Attrition
t = 0.94099, df = 187.08, p-value = 0.3479
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
 -3.316668  9.366557
sample estimates:
 mean in group No mean in group Yes 
         68.70130          65.67636 
t.test(PercentYrs_wManager ~ Attrition, data = cs2_conv2)

    Welch Two Sample t-test

data:  PercentYrs_wManager by Attrition
t = 3.2429, df = 188.9, p-value = 0.001399
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
  3.638589 14.938990
sample estimates:
 mean in group No mean in group Yes 
         41.57358          32.28479 
t.test(PercentYrs_inRole ~ Attrition, data = cs2_conv2)

    Welch Two Sample t-test

data:  PercentYrs_inRole by Attrition
t = 3.058, df = 189.5, p-value = 0.00255
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
  3.079205 14.270408
sample estimates:
 mean in group No mean in group Yes 
         42.37452          33.69971 
t.test(PercentYrs_inRoleAtComp ~ Attrition, data = cs2_conv2)

    Welch Two Sample t-test

data:  PercentYrs_inRoleAtComp by Attrition
t = 3.55, df = 177.46, p-value = 0.0004933
alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
95 percent confidence interval:
  5.468542 19.158856
sample estimates:
 mean in group No mean in group Yes 
          59.0657           46.7520


Based on the plots and t-test results, percent years in role at company (derived from years in role divided by years at company), seems like the most potentially useful of these derived variables.


I further explore the usefulness of the percent years in role at company by plotting combinations of percent years in role at company, monthly income, age, and job level. 


cs2_conv2 %>% ggplot(aes(x = PercentYrs_inRoleAtComp, y = MonthlyIncome, color = JobLevel)) +
  geom_point(alpha = 0.5, position = "jitter") + geom_smooth()


cs2_conv2 %>% ggplot(aes(x = PercentYrs_inRoleAtComp, y = Age, color = JobLevel)) +
  geom_point(alpha = 0.5, position = "jitter") + geom_smooth()


cs2_conv2 %>% ggplot(aes(x = MonthlyIncome, y = Age, color = JobLevel)) +
  geom_point(alpha = 0.5, position = "jitter") + geom_smooth()


Monthly income is a good predictor of job level (or vice versa) no matter the percent years in role at the company. Age is not as good (though there is some predictability). There is a much wider distribution of ages the lower the income, particularly under 5000.

Job level seems like a powerful predictor.


So far, the visual and statistical evidence and my best guess for top features leading to attrition are Job Level, Marital Status, Monthly Income and Overtime. To confirm this and/or narrow my list to 3, I want to use the list of 12 features that seem like they have the greatest differences between attrition categories. I generate all the unique combinations of 3 variables. Then using the loop in this code, I use each combination to build a Naive Bayes model to predict attrition, and rank them by how well each combination performed. 

modelIdx = c(2,15,16,17,19,20,24,29,30,33,34,36) #indexes of predicted top features
# these are the indexes for Age, JobInvolvement, JobLevel, JobRole, MaritalStatus, MonthlyIncome, OverTime, StockOptionLevel, TotalWorkingYears, YearsAtCompany, YearsInCurrentRole, YearsWithCurrManager

# initialize an empty data frame to store results
results = data.frame(Index1 = integer(), Index2 = integer(), Index3 = integer(), Sensitivity = numeric(), Specificity = numeric(), Accuracy = numeric(), stringsAsFactors = FALSE)

# number of different splits
iters = 50

# 70-30 train/test split
splitPerc = 0.7

# generate all combinations of 3 indexes
index_combinations = combinat::combn(modelIdx, 3)

# loop through each combination of 3 indexes
for (i in 1:ncol(index_combinations)) {
  index_set = index_combinations[, i]

  # create holders for the sensitivity, specificity, and accuracy for each iteration
  masterSens = numeric(iters)
  masterSpec = numeric(iters)
  masterAcc = numeric(iters)

  # iterate over the specified number of iterations
  for (j in 1:iters) {
    set.seed(j)

    # sample 70% for training
    trainIdx = sample(1:dim(cs2_conv2)[1], round(splitPerc * dim(cs2_conv2)[1]))
    # select the rows for training
    AttritionTrn = cs2_conv2[trainIdx, ]
    # select the remaining rows for testing
    AttritionTst = cs2_conv2[-trainIdx, ]

    # temporarily set the current indexes for modeling
    temp_modelIdx = index_set

    # train the model
    modelNB = naiveBayes(AttritionTrn[, temp_modelIdx], AttritionTrn$Attrition, laplace = 1)

    # predict using the model
    preds = predict(modelNB, AttritionTst[, temp_modelIdx])

    # make a confusion matrix
    CM = confusionMatrix(table(preds, AttritionTst$Attrition))

    # store sensitivity, specificity, and accuracy
    masterSens[j] = CM$byClass["Sensitivity"]
    masterSpec[j] = CM$byClass["Specificity"]
    masterAcc[j] = CM$overall["Accuracy"]
  }

  # calculate average sensitivity, specificity, and accuracy
  avg_sensitivity = mean(masterSens)
  avg_specificity = mean(masterSpec)
  avg_accuracy = mean(masterAcc)

  # store the results including the three indexes
  results = rbind(results, list(Index1 = index_set[1], Index2 = index_set[2], Index3 = index_set[3], Sensitivity = avg_sensitivity, Specificity = avg_specificity, Accuracy = avg_accuracy))
}

# output the results
results = results %>% arrange(-Specificity)
kable(head(results, 10), caption = "3 variable combos to predict attrition") %>% kable_styling(full_width = FALSE, position = "left")
3 variable combos to predict attrition
Index1 Index2 Index3 Sensitivity Specificity Accuracy
16 20 24 0.9409578 0.3656826 0.8475096
20 24 29 0.9571661 0.3050640 0.8511877
19 24 29 0.9470747 0.3003832 0.8422222
16 24 29 0.9722697 0.2859146 0.8607663
24 29 34 0.9593601 0.2833596 0.8495019
16 24 34 0.9585989 0.2794801 0.8483525
16 24 30 0.9544960 0.2769441 0.8440613
16 19 29 0.9107722 0.2750041 0.8068966
16 24 36 0.9586844 0.2522911 0.8435249
24 29 36 0.9626306 0.2439620 0.8453640


The top three features that predict attrition are within the group that I initially highlighted. They are Job Level, Monthly Income and Overtime. Stock Option Level and Marital Status are also strong predictors.

Obtaining marital status data may pose challenges due to potential privacy considerations, unlike the other predictors which are likely readily available through employment records.


This provides an overview of the first step of my analysis process focusing on visual evidence.

I started the analysis by plotting each variable separated by attrition group to compare their populations. Visually, the many features on this list seemed to show differences in these populations, but the four starred variables seemed particularly important.

Important features predicted by visual evidence:
Age
Business Travel
Distance from home
Department
Education Field
Environmental Satisfaction
Job Involvement
Job Level *
Job Role
Job Satisfaction
Marital Status *
Monthly Income *
Number Companies Worked For
Overtime *
Relationship Satisfaction
Stock Option Level
Total Working Years
Work Life Balance
Years At Company
Years In Current Role
Years With Current Manager

To illustrate an example of positive and negative visual evidence, I plot attrition by job level and gender. 

# plot positive predictors example: Job Level for presentation
# also plot negative predictor: Gender

# I revert to using my original converted dataset `cs2_conv`.

# plot positive predictor example: job level and attrition
# calculation of proportion of employees: employees in job level attrition yes / total employees in job level, to normalize each job level 
jobLevel_bar = cs2_conv %>%
  group_by(JobLevel, Attrition) %>%
  dplyr::summarize(n = n()) %>%
  mutate(prop = n / sum(n)) %>%
  filter(Attrition == "Yes") %>% 
  ggplot(aes(y = JobLevel, x = prop, fill = JobLevel)) +
  geom_bar(stat = "identity") +
  labs(y = "Job Level", x = "Proportion of Attrition",
       fill = "Job Level",
       title = "Proportion of Attrition within Each Job Level",
       caption = "Normalized by Total Employees per Job Level") +
  theme_bw() +
  scale_fill_brewer(palette = "Set1")
print(jobLevel_bar)

# ggsave(jobLevel_bar, filename = "plots/top3_jobLevel_bar.png")

# plot negative predictor example: gender and attrition
genderBar = cs2_conv %>% 
  group_by(Gender, Attrition) %>%
  dplyr::summarize(n = n()) %>%
  mutate(prop = n / sum(n)) %>%
  filter(Attrition == "Yes") %>% 
  ggplot(aes(y = Gender, x = prop)) +
  geom_bar(stat = "identity", fill = "#377EB8") + #fill color = Attrition group blue
  labs(y = "Gender", x = "Proportion of Attrition",
       fill = "Gender",
       title = "Proportion of Attrition within Each Gender",
       caption = "Normalized by Total Employees per Gender") +
  theme_bw() +
  theme(text = element_text(size = 12))
genderBar

# ggsave(genderBar, filename = "plots/top3negExample_genderBar.png")


Job level 1 has a much higher percent attrition than any other job level. Over a quarter of the employees in job level 1 leave the company. This is at least 13% higher than any other job level. Also of note, only 5% of employees in job level 4 leave.

On the other hand, gender doesn’t contribute to attrition. There is very little difference in attrition rates between males and females (17% and 15%).

This provides an overview of the other steps in my analysis process focusing on statistical evidence and modeling.
I tested for statistically significant differences in the attrition groups for each variable that was highlighted by visual evidence. For the numerical values, I used a t-test to predict the likelihood that the means of attrition groups are equal. For the categorical variables, I used a chi-square test to predict the likelihood that proportion of attrition is the same across categories of a variable.

These variables, including the four starred previously, had significant differences below the alpha 0.05 level.
Age
Job Involvement
Job Level *
Job Role
Marital Status *
Monthly Income *
Overtime *
Stock Option Level
Total Working Years
Years At Company
Years In Current Role
Years With Current Manager

From this list, I identified a subset of three variables that achieved the highest specificity when used in a predictive model for attrition. In the context of the model, specificity refers to the percentage of instances where attrition is correctly predicted.

The subset of three top factors that lead to attrition are Job Level, Monthly Income and Overtime.

# plot the other positive predictors for presentation: Monthly Income, Job Level and Overtime

# plot monthly income and attrition with a boxplot and two histograms
incomeBox = cs2_conv %>% 
  ggplot(aes(x = MonthlyIncome, y = Attrition, fill = Attrition)) +
  geom_boxplot() +
  ylab("Attrition") +
  theme_bw() +
  theme(legend.position = "none",
        axis.title.x = element_blank()) +
  scale_fill_brewer(palette = "Set1")

yAtt_hist = cs2_conv %>% filter(Attrition == "Yes") %>% 
  ggplot(aes(x = MonthlyIncome)) +
  geom_histogram(binwidth = 1000, fill = "#377EB8") +
  labs(title = "Distribution of Monthly Income by Employee Attrition",
       y = "Yes") +
  theme_bw() +
    theme(legend.position = "none",
          axis.title.x = element_blank())
  
nAtt_hist = cs2_conv %>% filter(Attrition == "No") %>% 
  ggplot(aes(x = MonthlyIncome)) +
  geom_histogram(binwidth = 1000, fill = "#E41A1C") +
  labs(#title = "Employee Attrition and Monthly Income",
       y = "No") +
  theme_bw() + 
  theme(legend.position = "none")

incomePlt = yAtt_hist / incomeBox / nAtt_hist
print(incomePlt)

# ggsave(incomePlt, filename = "plots/top3_incomeDist.png")


# make co-variation plots split by attrition groups

# plot positive predictor: job level and monthly income
income_jobLevel_box = ggplot(cs2_conv, aes(x = JobLevel, y = MonthlyIncome, fill = Attrition)) +
  geom_boxplot() +
  labs(x = "Job Level", y = "Monthly Income", fill = "Attrition") +
  ggtitle("Monthly Income by Job Level and Attrition") +
  theme_bw() + 
  scale_fill_brewer(palette = "Set1")
income_jobLevel_box

# ggsave(income_jobLevel_box, filename = "plots/top3_income_jobLevel_box.png")


# plot positive predictor: job level and attrition, with NO overtime
# employees NOT working overtime
jobLevel_OTno_bar = cs2_conv %>%
  group_by(OverTime, JobLevel, Attrition) %>%
  dplyr::summarize(n = n()) %>%
  mutate(prop = n / sum(n)) %>%
  filter(Attrition == "Yes" & OverTime == "No") %>%
  ggplot(aes(y = JobLevel, x = prop, fill = JobLevel)) +
  geom_bar(stat = "identity", position = "dodge") +
  labs(y = "Job Level", x = "Proportion of Attrition",
       fill = "Job Level",
       subtitle = "Proportion of Attrition within Each Job Level",
       title = "Employees with No Overtime Hours",
       caption = "Normalized by Total Employees per Job Level") +
  xlim(0.00, 0.55) +
  theme_bw() +
  theme(text = element_text(size = 12)) +
  scale_fill_brewer(palette = "Set1")
print(jobLevel_OTno_bar)

# ggsave(jobLevel_OTno_bar, filename = "plots/top3_jobLevel_OTno_bar.png")

# plot positive predictor: job level and attrition, with overtime
# employees working at least an hour of overtime
jobLevel_OTyes_bar = cs2_conv %>%
  group_by(OverTime, JobLevel, Attrition) %>%
  dplyr::summarize(n = n()) %>%
  mutate(prop = n / sum(n)) %>%
  filter(Attrition == "Yes" & OverTime == "Yes") %>%
  ggplot(aes(y = JobLevel, x = prop, fill = JobLevel)) +
  geom_bar(stat = "identity", position = "dodge") +
  labs(y = "Job Level", x = "Proportion of Attrition",
       fill = "Job Level",
       subtitle = "Proportion of Attrition within Each Job Level",
       title = "Employees Working Overtime",
       caption = "Normalized by Total Employees per Job Level") +
  xlim(0.00, 0.55) +
  theme_bw() +
  theme(text = element_text(size = 12)) +
  scale_fill_brewer(palette = "Set1")
print(jobLevel_OTyes_bar)

# ggsave(jobLevel_OTyes_bar, filename = "plots/top3_jobLevel_OTyes_bar.png")

# find 25th, 50th and 75th percentile of monthly incomes for each attrition group and job level
# is there a stay/go cut off for job level 4
mid50_income = cs2_conv %>%
  group_by(Attrition, JobLevel) %>%
  dplyr::summarise(q25 = quantile(MonthlyIncome, 0.25),
            median = median(MonthlyIncome),
            q75 = quantile(MonthlyIncome, 0.75))
kable(mid50_income, caption = "monthly income q25, median, q75 for each job level and attrition group") %>% kable_styling(full_width = FALSE, position = "left")
monthly income q25, median, q75 for each job level and attrition group
Attrition JobLevel q25 median q75
No 1 2293.00 2695.0 3207.0
No 2 4632.25 5365.5 6265.0
No 3 8624.50 9985.0 10911.5
No 4 13770.00 15992.0 16799.0
No 5 18844.00 19189.0 19636.0
Yes 1 2152.50 2424.5 2860.0
Yes 2 4712.25 5325.0 6162.5
Yes 3 7978.00 9582.0 10325.0
Yes 4 12552.50 12936.0 13065.0
Yes 5 19364.75 19695.0 19848.5


The plot of distributions of monthly income reveals a smaller income range and median income among employees that leave (in blue). The high-income outliers are likely due to factors like retirement.

The boxplot of job levels and income illustrates the positive relationship between these variables. It reveals a large income gap between employees that stay and those that leave in job level 4. Job levels 1 and 3 have a small trend of attrition with lower median incomes.

Attrition rates are low for all job levels in the graph of employees that do not work overtime, under 15% for job level 1 and under 10% for the others. However, the story changes for employees working at least an hour of overtime. Over 50% of employees in job level 1 working overtime choose to leave. This pattern holds true across all job levels except for job level 4, with attrition rates more than doubling among overtime workers.

# extra plots for the appendix

# plot positive predictor example: overtime and attrition
# calculation of proportion of employees: employees in overtime group & attrition yes / total employees in overtime group, to normalize each overtime group 
overtime_bar = cs2_conv %>%
  group_by(OverTime, Attrition) %>%
  dplyr::summarize(n = n()) %>%
  mutate(prop = n / sum(n)) %>%
  filter(Attrition == "Yes") %>% 
  ggplot(aes(y = OverTime, x = prop)) +
  geom_bar(stat = "identity", fill = "#377EB8") +
  labs(y = "Overtime", x = "Proportion of Attrition",
       fill = "Overtime",
       title = "Proportion of Attrition for Employees With and Without Overtime",
       caption = "Normalized by Total Employees per OT Group") +
  theme_bw() +
  scale_fill_brewer(palette = "Set1")
print(overtime_bar)

# ggsave(overtime_bar, filename = "plots/appendix/top3_overtime_bar.png")

# plot positive predictor: monthly income and overtime
income_OT_box = ggplot(cs2_conv, aes(x = OverTime, y = MonthlyIncome, fill = Attrition)) +
  geom_boxplot() +
  labs(x = "Overtime", y = "Monthly Income", fill = "Attrition") +
  ggtitle("Monthly Income by Overtime and Attrition") +
  theme_bw() +
  scale_fill_brewer(palette = "Set1")
print(income_OT_box)

# ggsave(income_OT_box, filename = "plots/appendix/top3_income_OT_box.png")


The attrition rate for overtime workers is more than three times that of employees that don’t work any overtime.

There is a larger income gap between attrition groups in employees working overtime, indicating a possibility that lower income and overtime make attrition more likely.


Top three factors leading to attrition: summary of trends, takeaways, and recommendations
Income
There is a large income gap between employees that stay and those that leave in job level 4. Those that leave have a median income just under 13,000, while those that stay have a median income of almost 16,000. Job levels 1 and 3 have a small trend of attrition with lower median incomes. Overall, the median income for employees that leave is smaller than that of those that stay.

Job Level
Over a quarter of the employees in job level 1 leave the company, a much higher attrition rate than any other job level.

Overtime
Over 50% of employees in job level 1 working overtime choose to leave. This pattern holds true across all job levels except for job level 4, with attrition rates more than doubling among overtime workers.

Recommendations
Job level 4, if below 14,000, increase monthly pay. For all other job levels, reduce overtime. Job level 1 increase pay and promote to job level 2.


Objective 2: Identify job role specific trends.


For each numerical variable, I plot the job roles in side-by-side box plots. Using bar plots, I plot the proportion of the levels of each categorical variable grouped by job roles. 

# reorder levels of JobRole from low income/level to high
cs2_conv$JobRole = factor(cs2_conv$JobRole, levels = c("Sales Representative", "Laboratory Technician", "Human Resources", "Research Scientist", "Sales Executive", "Healthcare Representative", "Manufacturing Director", "Research Director", "Manager"))

# rename numerical and categorical variables for nicer axis titles
custom_labels = list(
  JobLevel = "Job Level",
  JobRole = "Job Role",
  MaritalStatus = "Marital Status",
  MonthlyIncome = "Monthly Income",
  OverTime = "Overtime",
  StockOptionLevel = "Stock Option Level",
  TotalWorkingYears = "Total Working Years",
  YearsAtCompany = "Years At Company",
  YearsInCurrentRole = "Years in Current Role",
  YearsWithCurrManager = "Years with Current Manager"
)

# a function to get the appropriate label from the list above
get_label = function(var) {
  if (var %in% names(custom_labels)) {
    return(custom_labels[[var]])
  } else {
    return(var)
  }
}

# numerical_columns = colnames(cs2_numerical)
for (numvar in numerical_columns) {
  boxplot = cs2_conv %>%  
    ggplot(aes(x = .data[[numvar]], y = JobRole, fill = JobRole)) +
    geom_boxplot() +
    labs(title = paste("Job Role vs", get_label(numvar)),
         x = get_label(numvar), y = "Job Role") +
    theme_bw() +
    theme(legend.position = "none",
          text = element_text(size = 12)) +
    scale_fill_brewer(palette = "Spectral")
  
  # display each plot
  print(boxplot)
  
  # create a unique filename for each plot
  filename = paste0("plots/JobRole/boxplt_JobRole_vs_", numvar, ".png")
  
  # save the plots
  # ggsave(filename, plot = boxplot, device = "png")
}

# categorical_columns = colnames(cs2_categorical)
cat_cols = categorical_columns[!categorical_columns %in% "JobRole"]

for (catvar in cat_cols) {
  barplot = cs2_conv %>%
    group_by(JobRole, .data[[catvar]], .drop = FALSE) %>%
    dplyr::summarize(count = n(), .groups = 'drop') %>%
    group_by(JobRole) %>%
    mutate(prop = count / sum(count)) %>%
    ggplot(aes(y = JobRole, x = prop, fill = .data[[catvar]])) +
    geom_bar(stat = "identity", position = "dodge") +
    labs(title = paste("Job Role vs", get_label(catvar)),
         y = "Job Role", x = "Proportion", fill = get_label(catvar)) +
    theme_bw() +
    theme(legend.position = "right",
          text = element_text(size = 12)) +
    scale_fill_brewer(palette = "Set1")
  
  #display each plot
  print(barplot)
  
  # create a unique filename for each plot
  filename = paste0("plots/JobRole/barplot_JobRole_vs_", catvar, ".png")
  
  # save the plots
  # ggsave(filename, plot = barplot, device = "png")
}


Trends in Job Roles

  1. Attrition, Tenure and Role Duration:
  1. Income Distribution:
  1. Job Level:
  1. Age:
  1. Training, Promotion and Salary Increase:
  1. Monthly, Daily and Hourly Rates:
  1. Employee Demographics:
  1. Job Involvement and Satisfaction:
  1. Marital Status:
  1. Education:
  1. Job Roles & Departmental Breakdown:

As job roles seem to segregate into 3 groups by monthly income and other factors like job level, years in current role, with manager and at company, total working years and to a lesser extent age, I make a new median income level variable and group them into low, middle and high levels. Then I use a t-test to see if the difference in mean incomes between the pairs of levels (low vs. mid and mid vs. high) are significantly different. I also plot the derived variables Percent work years at company and Percent year in role at company vs the job roles and run t-tests to check for differences in these mean percents between the grouped income levels. 

# reorder levels of JobRole
cs2_conv2$JobRole = factor(cs2_conv2$JobRole, levels = c("Sales Representative", "Laboratory Technician", "Human Resources", "Research Scientist", "Sales Executive", "Healthcare Representative", "Manufacturing Director", "Research Director", "Manager"))

# group roles by median income level (low, med, high)
# test difference in salary between low and mid and mid and high
cs2_conv2 = cs2_conv2 %>% 
  mutate(incomeGroup = case_when(
      JobRole %in% c("Sales Representative", "Research Scientist", "Human Resources", "Laboratory Technician") ~ "Low",
      JobRole %in% c("Sales Executive", "Manufacturing Director", "Healthcare Representative") ~ "Medium",
      TRUE ~ "High"
    )
  ) %>%
  mutate(incomeGroup = factor(incomeGroup, levels = c("Low", "Medium", "High")))

# check the conversion
# head(cs2_conv2)

# filter the data
cs2_LowMid = cs2_conv2 %>% filter(incomeGroup != "High")
cs2_MidHigh = cs2_conv2 %>% filter(incomeGroup != "Low")

# perform t-tests
t_test_LowMid = t.test(MonthlyIncome ~ incomeGroup, data = cs2_LowMid)
t_test_MidHigh = t.test(MonthlyIncome ~ incomeGroup, data = cs2_MidHigh)

# print the results
t_test_LowMid

    Welch Two Sample t-test

data:  MonthlyIncome by incomeGroup
t = -27.646, df = 522.61, p-value < 2.2e-16
alternative hypothesis: true difference in means between group Low and group Medium is not equal to 0
95 percent confidence interval:
 -4268.293 -3701.937
sample estimates:
   mean in group Low mean in group Medium 
            3167.491             7152.606 
t_test_MidHigh

    Welch Two Sample t-test

data:  MonthlyIncome by incomeGroup
t = -31.529, df = 152.77, p-value < 2.2e-16
alternative hypothesis: true difference in means between group Medium and group High is not equal to 0
95 percent confidence interval:
 -9904.980 -8736.867
sample estimates:
mean in group Medium   mean in group High 
            7152.606            16473.529


Unsurprisingly, there is overwhelming evidence that mean incomes between income groups are significantly different.

For follow-up
It would be interesting to follow-up by plotting the 3 income groups and income or other features of interest split by attrition groups. Also, it would be good to investigate trends in income, job level, and overtime between the different attrition groups in different job roles.


Objective 3: Build a model to predict attrition.

(with a minimum of 60% sensitivity and 60% specificity)

I start with a Naive Bayes model to predict attrition. There are 33 possible explanatory features in the data set. I choose to start with the 18 that earlier analyses suggest may be significantly different between the attrition groups. The goal with this block of code is to build an externally validated model with 100 different train/test splits of those 18 features. Then using intuition from earlier analyses, I remove one feature at a time, until I have maximized the specificity of the model. 

# Naive Bayes classifier
# start with lots of explanatory variables and distill down manually one at a time using domain knowledge

# str(cs2_conv2) #this is the dataframe with my derived variables too


# list indexes of explanatory variables 

# for reference:
# modelIdx = c(2,4:9,11:19,21,22,25:27,29:40) #list of all possible features
# modelIdx = c(16,19,20,24,29) #top 5 features

# start here: list of indexes of 18 significant variables (alpha = 0.05) from t-tests and chi-square tests
# modelIdx = c(2,4,6,7,12,15,16,17,18,19,20,24,29,30,32,33,34,36) #significant features: sens 85.6%, spec 60.7%

# end here: list of indexes which produced highest specificity, derived manually
modelIdx = c(12,15,16,17,19,20,24,29,30,32,33,34,36) #sensitivity: 84.4% specificity: 62.3%

# other promising combinations:
# modelIdx = c(2,12,15,16,17,19,20,24,29,30,32,33,34,36) #84.2, 61.4
# modelIdx = c(12,15,16,17,20,24,29,30,32,33,34,36) #84.6, 61.3
# modelIdx = c(15,16,17,20,24,29,30,32,33,34,36) #84, 60.5


# list the explanatory variables used
names(cs2_conv2[,modelIdx])
 [1] "EnvironmentSatisfaction" "JobInvolvement"         
 [3] "JobLevel"                "JobRole"                
 [5] "MaritalStatus"           "MonthlyIncome"          
 [7] "OverTime"                "StockOptionLevel"       
 [9] "TotalWorkingYears"       "WorkLifeBalance"        
[11] "YearsAtCompany"          "YearsInCurrentRole"     
[13] "YearsWithCurrManager"   
# how many explanatory variables are used
length(modelIdx)
[1] 13
# 100 different splits
iters = 100

# make holders for the stats from each iteration
masterAccu = matrix(nrow = iters, ncol = 2)
masterPval = matrix(nrow = iters, ncol = 2)
masterSens = matrix(nrow = iters, ncol = 2)
masterSpec = matrix(nrow = iters, ncol = 2)

# 70-30 train/test split
splitPerc = .7

for(i in 1:iters)
{
  set.seed(i)
  
  # sample 70%
  trainIdx = sample(1:dim(cs2_conv2)[1], round(splitPerc*dim(cs2_conv2)[1]))
  # choose the rows that match those sampled numbers for training
  AttritionTrn = (cs2_conv2[trainIdx,])
  # and the others for testing
  AttritionTst = (cs2_conv2[-trainIdx,])
  
  # head(AttritionTrn)
  # head(AttritionTst)
  
  # give the model the training variables, training labels
  modelNB = naiveBayes(AttritionTrn[,modelIdx], AttritionTrn$Attrition, laplace = 1)
  
  # use the model and testing explanatory variables (modelIdx) to predict the testing labels
  preds = predict(modelNB, AttritionTst[,modelIdx])
  
  # make a confusion matrix comparing the predicted labels to the true labels
  # predicted labels = rows, true labels = cols
  CM = confusionMatrix(table(preds, AttritionTst$Attrition))
  
  masterAccu[i,] = c(i, CM$overall["Accuracy"])
  masterPval[i,] = c(i, CM$overall["AccuracyPValue"])
  masterSens[i,] = c(i, CM$byClass["Sensitivity"])
  masterSpec[i,] = c(i, CM$byClass["Specificity"])
}

# organize the output data
colnames(masterAccu) = c("Seed", "Accuracy")
colnames(masterPval) = c("Seed", "AccuracyPValue")
colnames(masterSens) = c("Seed", "Sensitivity")
colnames(masterSpec) = c("Seed", "Specificity")
NB_results = merge(as.data.frame(masterAccu), as.data.frame(masterPval), by = "Seed", all = TRUE)
NB_results = merge(NB_results, as.data.frame(masterSens), by = "Seed", all = TRUE)
NB_results = merge(NB_results, as.data.frame(masterSpec), by = "Seed", all = TRUE)

NB_stats = colMeans(NB_results[,2:5])
NB_stats = data.frame(
  Metric = c("Accuracy", "AccuracyPValue", "Sensitivity", "Specificity"),
  Value = c(sprintf("%.1f%%", NB_stats[1]*100),
            sprintf("%.2e", NB_stats[2]),
            sprintf("%.1f%%", NB_stats[3]*100),
            sprintf("%.1f%%", NB_stats[4]*100)))

# output the metrics of the naive bayes model
cat("Naive Bayes \n")
Naive Bayes 
cat("Accuracy:", NB_stats[1,2], "\n")
Accuracy: 80.9% 
cat("Accuracy P-Value:", NB_stats[2,2], "\n")
Accuracy P-Value: 7.83e-01 
cat("Sensitivity:", NB_stats[3,2], "\n")
Sensitivity: 84.4% 
cat("Specificity:", NB_stats[4,2], "\n")
Specificity: 62.3%


I start with these 18 features: Age, BusinessTravel, Department, DistanceFromHome, EnvironmentSatisfaction, JobInvolvement, JobLevel, JobRole, JobSatisfaction, MaritalStatus, MonthlyIncome, OverTime, StockOptionLevel, TotalWorkingYears, WorkLifeBalance, YearsAtCompany, YearsInCurrentRole, YearsWithCurrManager.

Using the method described above, I am able to achieve the highest specificity of 62.3% and a combined sensitivity and specificity of 146.7 with 13 features: EnvironmentSatisfaction, JobInvolvement, JobLevel, JobRole, MaritalStatus, MonthlyIncome, OverTime, StockOptionLevel, TotalWorkingYears, WorkLifeBalance, YearsAtCompany, YearsInCurrentRole, YearsWithCurrManager.


Then I attempt to validate my predicted best features for the model with help from chatGPT. I asked chatGPT to help me write a nested loop that would find every combination of a defined number of features, rank them by highest specificity and return the top ten combinations. For each iteration of the loop, I asked it to increase the number of features by one, breaking out of the loop when the specificity stopped increasing. This is very computationally heavy, and there is a bug in the code when outputting results related to breaking out of the loop. 

# perhaps it would be more efficient to do the train test splits on the outer loop?
# also I should place the progress reporter (Sys.time()) in a different place in the code

# Function to calculate sensitivity, specificity for all combinations of a given number of variables
calculate_combinations <- function(modelIdx, max_vars = 18, iters = 10, splitPerc = 0.7) {
  
  # Initialize an empty list to store results
  results_list <- list()
  
  # Initialize a variable to keep track of the maximum specificity reached
  max_specificity_so_far <- 0
  
  # Initialize a variable to store the maximum mean specificity from previous iterations
  max_mean_specificity_previous <- 0

  # Loop over different number of variables
  for (num_vars in seq(8, max_vars)) {
    cat("Number of variables:", num_vars, "\n")
    start_time <- Sys.time()
    
    # Generate all combinations of variables
    index_combinations <- combinat::combn(modelIdx, num_vars)
    
    # Initialize an empty list to store results for this iteration
    temp_results_list <- list()
    
    # Loop through each combination of variables
    for (i in 1:ncol(index_combinations)) {
      index_set <- index_combinations[, i]
      
      # Create holders for the sensitivity, specificity for each iteration
      masterSens <- numeric(iters)
      masterSpec <- numeric(iters)
      
      # Iterate over the specified number of iterations
      for (j in 1:iters) {
        set.seed(j)
        
        # Sample 70% for training
        trainIdx <- sample(1:dim(cs2_conv2)[1], round(splitPerc * dim(cs2_conv2)[1]))
        # Select the rows for training
        AttritionTrn <- cs2_conv2[trainIdx, ]
        # Select the remaining rows for testing
        AttritionTst <- cs2_conv2[-trainIdx, ]
        
        # Temporarily set the current indexes for modeling
        temp_modelIdx <- index_set
        
        # Train the model
        modelNB <- naiveBayes(AttritionTrn[, temp_modelIdx], AttritionTrn$Attrition, laplace = 1)
        
        # Predict using the model
        preds <- predict(modelNB, AttritionTst[, temp_modelIdx])
        
        # Confusion matrix
        CM <- confusionMatrix(table(preds, AttritionTst$Attrition))
        
        # Store sensitivity, specificity
        masterSens[j] <- CM$byClass["Sensitivity"]
        masterSpec[j] <- CM$byClass["Specificity"]
      }
      
      # Average sensitivity, specificity
      avg_sensitivity <- mean(masterSens)
      avg_specificity <- mean(masterSpec)
      
      # Store the results including the combination of variables
      temp_results_list[[i]] <- list(variables = index_set, Sensitivity = avg_sensitivity, Specificity = avg_specificity)
    }
    
    end_time <- Sys.time()
    time_taken <- end_time - start_time
    cat("Time taken:", time_taken, "\n")
    
    # Store the results for this iteration
    results_list[[num_vars]] <- temp_results_list
    
    # Get the maximum mean specificity for this number of variables
    max_mean_specificity_current <- max(sapply(temp_results_list, function(x) x$Specificity))
    
    # Check if the maximum mean specificity for the current number of variables is less than the previous maximum
    if (max_mean_specificity_current < max_mean_specificity_previous) {
      cat("Maximum specificity reached for", num_vars, "variables is less than previous maximum. Stopping further iterations.\n")
      break
    }
    
    # Update the maximum mean specificity from previous iterations
    max_mean_specificity_previous <- max_mean_specificity_current
  }
  
  return(results_list)
}

# Define the list of indexes to loop through
modelIdx <- c(2,4,6,7,12,15,16,17,18,19,20,24,29,30,32,33,34,36) #significant features

# Define the maximum number of variables
max_vars <- 18

# Call the function to calculate combinations
results <- calculate_combinations(modelIdx, max_vars)

# Determine the maximum expected number of combinations
max_combinations <- max_vars * 10  # Assuming a maximum of 10 combinations per number of variables

# Preallocate the output data frame with maximum expected number of rows
output_df <- data.frame(Number_of_Variables = integer(max_combinations),
                        Variable_Indexes = character(max_combinations),
                        Mean_Sensitivity = numeric(max_combinations),
                        Mean_Specificity = numeric(max_combinations),
                        Sum_of_Sensitivity_and_Specificity = numeric(max_combinations),
                        stringsAsFactors = FALSE)

# Loop over different number of variables
for (num_vars in seq(8, max_vars)) {
  cat("\nTop 10 combinations with the highest specificity for", num_vars, "variables:\n")

  sorted_indices <- order(sapply(results[[num_vars]], function(x) x$Specificity), decreasing = TRUE)
  for (i in 1:min(10, length(sorted_indices))) {
    index <- sorted_indices[i]
    cat("Combination", i, ": Variables =", results[[num_vars]][[index]]$variables, ", Specificity =", results[[num_vars]][[index]]$Specificity, "\n")

    # Assign the results to the preallocated rows in the output data frame
    row_index <- (num_vars - 10) * 10 + i  # Calculate the row index
    output_df$Number_of_Variables[row_index] <- num_vars
    output_df$Variable_Indexes[row_index] <- paste(results[[num_vars]][[index]]$variables, collapse = ", ")
    output_df$Mean_Sensitivity[row_index] <- results[[num_vars]][[index]]$Sensitivity
    output_df$Mean_Specificity[row_index] <- results[[num_vars]][[index]]$Specificity
    output_df$Sum_of_Sensitivity_and_Specificity[row_index] <- results[[num_vars]][[index]]$Sensitivity + results[[num_vars]][[index]]$Specificity
  }
}

# Print the final output data frame
print(output_df)


This is useful for a few reasons. It confirms that the 13 variables I chose modelIdx = c(12,15,16,17,19,20,24,29,30,32,33,34,36) result in the highest specificity (61.7%) for all combinations of 13 variables. It also returns higher specificity, 62.6% with 14 variables, the 13 above, plus Department (index 6) and 62.2% with 15 variables, the 13 above, plus BusinessTravel and DistanceFromHome (indexes 4 and 7).


I want to use several of the best combinations of explanatory variables to try to tune the laplace smoothing parameter. I also want to see if I can adjust and tune the thresholding, because the dataset is unbalanced with only 16% “Yes” in the Attrition variable. I evaluate all combinations of variables and tuning parameters by averaging external and internal validation results. 

# computationally expensive, not sure how to do it a better way

# define parameters (the ones I really used)
# modelIdx_list = list(
#   c(2, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36),      # Combination 1
#   c(12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36),         # Combination 2
#   c(6, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36),      # Combination 3
#   c(4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36),   # Combination 4
#   c(4, 6, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36) # Combination 5
# )
# alphas = seq(0.1, 1, 0.1) #smoothing parameters to try
# thresholds = seq(0.1, 0.6, 0.02) #classifier thresholds to try for "Yes" based on ~0.16 proportion yes to no
# iters = 100  #train/test split iterations
# splitPerc = 0.7  #percentage of data for training

# define shortened parameters for demo purposes
modelIdx_list = list(
  c(12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36),         # Combination 2 (my hand-picked variables)
  c(4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36)    # Combination 4 (the *best*)
)
alphas = seq(0.1, 0.9, 0.2) #smoothing parameters to try
thresholds = seq(0.3, 0.5, 0.05) #classifier thresholds to try for "Yes" based on ~0.16 proportion yes to no
iters = 10  #train/test split iterations
splitPerc = 0.7  #percentage of data for training

# initialize a list to store results
results_list = list()

# time the loop 
loop_start = Sys.time()

# loop through modelIdx combinations
for (modelIdx in modelIdx_list) {
  
  # loop through the alphas
  for (alpha in alphas) {
    
    # loop through the thresholds
    for (threshold in thresholds) {
      
      # time the threshold loop
      thresh_start = Sys.time()
      
      # make holders for the stats from each iteration for this modelIdx, alpha, and threshold
      iteration_stats = matrix(nrow = iters, ncol = 5)
      colnames(iteration_stats) = c("Seed", "Threshold", "Alpha", "Sensitivity", "Specificity")
      
      # counter for row index in iteration_stats
      row_counter = 1
      
      # external cross-validation loop
      for (i in 1:iters) {

        set.seed(i)

        # generate the test train split
        trainIdx = sample(1:nrow(cs2_conv), round(splitPerc * nrow(cs2_conv)))
        AttritionTrn = cs2_conv[trainIdx, ]
        AttritionTst = cs2_conv[-trainIdx, ]

        # train Naive Bayes model with current alpha and feature (modelIdx) set
        modelNB = naiveBayes(AttritionTrn[, modelIdx], AttritionTrn$Attrition, laplace = alpha)

        # predict on testing set
        preds = predict(modelNB, AttritionTst[, modelIdx], type = "raw") # raw returns the probabilities

        attrition_probs = preds[, "Yes"]

        predictions = ifelse(attrition_probs >= threshold, "Yes", "No")

        # calculate confusion matrix
        CM_no = confusionMatrix(table(predictions, AttritionTst$Attrition))

        # get sensitivity and specificity for "No" class
        sens_no = CM_no[4]$byClass["Sensitivity"] # because reference (positive class) is set to no
        spec_no = CM_no[4]$byClass["Specificity"]

        # store results for that iteration
        iteration_stats[row_counter, ] = c(i, threshold, alpha, sens_no, spec_no)
        row_counter = row_counter + 1

      } # complete external cross-validation loop
      
      # initialize variables to store predictions and actual values to calculate confusion matrix after all LOO
      all_predictions = c()
      all_actual = c()
      
      # internal cross-validation loop (Leave-One-Out Cross-Validation)
      for (row in 1:nrow(cs2_conv)) {
        
        # generate the test train split
        AttritionTrn = cs2_conv[-row, ]
        AttritionTst = cs2_conv[row, ]
        
        # train Naive Bayes model with current alpha and feature (modelIdx) set
        modelNB = naiveBayes(AttritionTrn[, modelIdx], AttritionTrn$Attrition, laplace = alpha)
        
        # predict on testing set
        preds = predict(modelNB, AttritionTst[, modelIdx], type = "raw") # raw returns the probabilities
        
        attrition_probs = preds[,"Yes"]
        attrition_probs = attrition_probs[["Yes"]] # get just the probability from the named number

        predictions = ifelse(attrition_probs >= threshold, "Yes", "No")
        
        # accumulate predictions and actual values
        all_predictions = c(all_predictions, predictions)
        all_actual = c(all_actual, as.character(AttritionTst$Attrition)) # turn factors to characters to match all_actual
        
      } # complete internal cross-validation loop

      # calculate confusion matrix using all predictions and actual values
      CM_no = confusionMatrix(table(all_predictions, all_actual))
      
      # get sensitivity and specificity for "No" class
      sens_icv = CM_no[4]$byClass["Sensitivity"] # because reference (positive class) is set to no
      spec_icv = CM_no[4]$byClass["Specificity"]
      
      # calculate mean sensitivity and specificity over ECV and ICV for this combination of modelIdx, alpha, and threshold
      # not sure if this is the best way since there are many more test/train splits in ICV
      # also don't know if people ever really average ECV and ICV results
      avg_sens = mean(c(mean(iteration_stats[, "Sensitivity"]), sens_icv))
      avg_spec = mean(c(mean(iteration_stats[, "Specificity"]), spec_icv))
      
      # store results for this combination of modelIdx, alpha, and threshold
      results_list = c(results_list, list(
        data.frame(
          ModelIdx = toString(modelIdx),
          Alpha = alpha,
          Threshold = threshold,
          AvgSensitivity = avg_sens,
          AvgSpecificity = avg_spec,
          AvgSum = avg_sens + avg_spec
        )
      ))

        # time the threshold loop
        thresh_end = Sys.time()
        time_taken_thresh = difftime(thresh_end, thresh_start, units = "secs")
        cat("Threshold Loop Time:", time_taken_thresh, "secs \n")
        cat("ModelIdx:", toString(modelIdx), "- Alpha:", alpha, "- Threshold:", threshold, "\n")
      
    } # complete threshold loop

  } # complete alpha loop
  
} # complete modelIdx loop
Threshold Loop Time: 5.295719 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.3 
Threshold Loop Time: 6.194655 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.35 
Threshold Loop Time: 5.935995 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.4 
Threshold Loop Time: 5.645946 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.45 
Threshold Loop Time: 6.093287 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.5 
Threshold Loop Time: 7.394172 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.3 
Threshold Loop Time: 6.354893 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.35 
Threshold Loop Time: 6.575595 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.4 
Threshold Loop Time: 8.486059 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.45 
Threshold Loop Time: 6.610982 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.5 
Threshold Loop Time: 6.496804 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.3 
Threshold Loop Time: 5.527282 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.35 
Threshold Loop Time: 5.098834 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.4 
Threshold Loop Time: 5.023465 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.45 
Threshold Loop Time: 5.168213 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.5 
Threshold Loop Time: 6.979724 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.3 
Threshold Loop Time: 5.39098 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.35 
Threshold Loop Time: 5.22696 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.4 
Threshold Loop Time: 5.094164 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.45 
Threshold Loop Time: 5.199527 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.5 
Threshold Loop Time: 5.625987 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.3 
Threshold Loop Time: 5.951124 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.35 
Threshold Loop Time: 6.278088 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.4 
Threshold Loop Time: 5.896067 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.45 
Threshold Loop Time: 7.065845 secs 
ModelIdx: 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.5 
Threshold Loop Time: 7.367793 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.3 
Threshold Loop Time: 10.19007 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.35 
Threshold Loop Time: 7.363244 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.4 
Threshold Loop Time: 7.143034 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.45 
Threshold Loop Time: 7.580932 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.1 - Threshold: 0.5 
Threshold Loop Time: 5.714779 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.3 
Threshold Loop Time: 6.387567 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.35 
Threshold Loop Time: 6.194161 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.4 
Threshold Loop Time: 7.325557 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.45 
Threshold Loop Time: 6.228531 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.3 - Threshold: 0.5 
Threshold Loop Time: 6.639477 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.3 
Threshold Loop Time: 6.100348 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.35 
Threshold Loop Time: 6.430035 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.4 
Threshold Loop Time: 6.722585 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.45 
Threshold Loop Time: 6.185506 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.5 - Threshold: 0.5 
Threshold Loop Time: 5.689047 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.3 
Threshold Loop Time: 5.658677 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.35 
Threshold Loop Time: 6.963918 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.4 
Threshold Loop Time: 6.851558 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.45 
Threshold Loop Time: 6.431898 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.7 - Threshold: 0.5 
Threshold Loop Time: 6.668972 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.3 
Threshold Loop Time: 6.705194 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.35 
Threshold Loop Time: 7.238828 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.4 
Threshold Loop Time: 6.780722 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.45 
Threshold Loop Time: 6.329726 secs 
ModelIdx: 4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 - Alpha: 0.9 - Threshold: 0.5 
# loop time
loop_end = Sys.time()
time_taken_loop = difftime(loop_end, loop_start, units = "mins")
cat("Total Loop Time:", time_taken_loop, "mins \n")
Total Loop Time: 5.326095 mins 
# convert results_list to a data frame
results_df = do.call(rbind, results_list)

# output top 10 combinations for each ModelIdx
top_10_combos = results_df %>%
  arrange(ModelIdx, desc(AvgSum), desc(AvgSpecificity), desc(AvgSensitivity)) %>%
  group_by(ModelIdx) %>%
  #top_n(10, wt = AvgSum)
  #make a shorter version for demo purpose
  top_n(5, wt = AvgSum)
kable(top_10_combos, caption = "demo top 10 sensitivity + specificity tuned parameter combos") %>% kable_styling(full_width = FALSE, position = "left")
demo top 10 sensitivity + specificity tuned parameter combos
ModelIdx Alpha Threshold AvgSensitivity AvgSpecificity AvgSum
12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.1 0.50 0.8390322 0.6387663 1.477798
12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.5 0.50 0.8415109 0.6349447 1.476455
12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.3 0.50 0.8403885 0.6349447 1.475333
12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.9 0.50 0.8417456 0.6335161 1.475262
12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.7 0.50 0.8401521 0.6349447 1.475097
4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.7 0.45 0.8244917 0.6559893 1.480481
4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.9 0.45 0.8242569 0.6559893 1.480246
4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.5 0.45 0.8235836 0.6559893 1.479573
4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.3 0.45 0.8228953 0.6559893 1.478884
4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.1 0.45 0.8210799 0.6547697 1.475850


Based on this parameter tuning, the highest sum of sensitivity and specificity scores my Naive Bayes model achieves is 148.79 (Sensitivity of 83.11% and Specificity of 65.68%). The optimization was achieved with ModelIdx = c(4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36), which are the indexes of the columns in cs2_conv, alpha = 0.7 and threshold (of "Yes" >=) = 0.46. The variables are BusinessTravel, DistanceFromHome, EnvironmentSatisfaction, JobInvolvement, JobLevel, JobRole, MaritalStatus, MonthlyIncome, OverTime, StockOptionLevel, TotalWorkingYears, WorkLifeBalance, YearsAtCompany, YearsInCurrentRole, YearsWithCurrManager. Now, I will train my model using these and the full data set and use that to predict the labels on the competition set.


I would like to compare a k-Nearest Neighbors (k-NN) model to the Naive Bayes model. I want to see if I can use k-NN with both numerical and categorical variables, or just numerical (maybe convert the numerical factors back to numbers). Another option would be to fit separate models to each category in the categorical variables. I may want to experiment with the explanatory variables used, scale the variables, try ECV + ICV, tune k, tune the threshold or over or under-sample. I start by transforming the variables. 

# starting with the original dataset `cs2` since the ordinal categorical variables are in an integer class
# there are a few other variables that I could transform into ranked like business travel
# not sure it is valid to do it for marital status or overtime

# make a copy of the original dataset
numerical_df = cs2

# check the data
# head(numerical_df$BusinessTravel)

# reorder factor levels
numerical_df$BusinessTravel = factor(numerical_df$BusinessTravel, levels = c("Non-Travel", "Travel_Rarely", "Travel_Frequently"), labels = c("Non-Travel", "Travel_Rarely", "Travel_Frequently"))

# rename the levels to numbers
levels(numerical_df$BusinessTravel) = c(1:3)

# convert factor to integer
numerical_df$BusinessTravel = as.integer(numerical_df$BusinessTravel)

# check the conversion
# head(numerical_df$BusinessTravel)

# repeat for marital status and overtime :/
# head(numerical_df$MaritalStatus)
numerical_df$MaritalStatus = factor(numerical_df$MaritalStatus, levels = c("Single", "Married", "Divorced"), labels = c("Single", "Married", "Divorced"))
levels(numerical_df$MaritalStatus) = c(1:3)
numerical_df$MaritalStatus = as.integer(numerical_df$MaritalStatus)
# head(numerical_df$MaritalStatus)

# head(numerical_df$OverTime)
numerical_df$OverTime = factor(numerical_df$OverTime, levels = c("Yes", "No"), labels = c("Yes", "No"))
levels(numerical_df$OverTime) = c(1:2)
numerical_df$OverTime = as.integer(numerical_df$OverTime)
# head(numerical_df$OverTime)

# scale the variables
# str(numerical_df)
# list of columns to exclude from scaling
exclude_columns = c("ID", "EmployeeCount", "EmployeeNumber", "StandardHours")
# scale the numeric variables and reassign values to same columns
numerical_df = numerical_df %>%
  mutate_at(vars(-matches(paste(exclude_columns, collapse = "|"))), 
            .funs = function(x) if(is.numeric(x)) scale(x) else x)
# str(numerical_df)



This is a modified version of the NB variable optimization code block from above. I start with the variables with evidence of signficant (p < 0.05) differences between the attrition groups. They are either integers or I can reasonably order their levels and tranform them into integers. If they can’t reasonably be ordered, for example department and job role, I don’t include them. This loop finds all the unique combinations of a specified number of these scaled, numeric variables. It iterates through a number of train/test splits and finds the mean sensitivity, specificity and sum of those for each combination for that number of variables. It returns the top ten combinations for that number of variables. Then each loop increases the number of variables used in the model by one. 

# this is a computationally heavy, lengthy process depending on iterations.

modelIdx_num = c(2, 4, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 32, 33, 34, 36) # sig numeric vars (16)

# Function to calculate sensitivity, specificity for all combinations of a given number of variables
calculate_combinations <- function(modelIdx, max_vars = 15, iters = 10, splitPerc = 0.7) {
  # Initialize an empty list to store results
  results_list <- list()
  
  # Initialize a variable to keep track of the maximum specificity reached
  # max_specificity_so_far <- 0
  
  # Initialize a variable to store the maximum mean specificity from previous iterations
  # max_mean_specificity_previous <- 0

  # Loop over different number of variables
  for (num_vars in seq(8, max_vars)) {
    cat("Number of variables:", num_vars, "\n")
    start_time <- Sys.time()
    
    # Generate all combinations of variables
    index_combinations <- combinat::combn(modelIdx, num_vars)
    
    # Initialize an empty list to store results for this iteration
    temp_results_list <- list()
    
    # Loop through each combination of variables
    for (i in 1:ncol(index_combinations)) {
      index_set <- index_combinations[, i]
      
      # Create holders for the sensitivity, specificity for each iteration
      masterSens <- numeric(iters)
      masterSpec <- numeric(iters)
      
      # Iterate over the specified number of iterations
      for (j in 1:iters) {
        set.seed(j)
        
        # Sample 70% for training
        trainIdx <- sample(1:dim(numerical_df)[1], round(splitPerc * dim(numerical_df)[1]))
        # Select the rows for training
        AttritionTrn <- numerical_df[trainIdx, ]
        # Select the remaining rows for testing
        AttritionTst <- numerical_df[-trainIdx, ]
        
        # Temporarily set the current indexes for modeling
        temp_modelIdx <- index_set
        
        # Train the model
        classifications <- knn(AttritionTrn[, temp_modelIdx], AttritionTst[, temp_modelIdx], AttritionTrn$Attrition, prob = TRUE, k = 15)

        # Predict using the model
        # preds <- predict(modelNB, AttritionTst[, temp_modelIdx])

        # Confusion matrix
        CM <- confusionMatrix(table(classifications, AttritionTst$Attrition))
        
        # Store sensitivity, specificity
        masterSens[j] <- CM$byClass["Sensitivity"]
        masterSpec[j] <- CM$byClass["Specificity"]
      }
      
      # Average sensitivity, specificity
      avg_sensitivity <- mean(masterSens)
      avg_specificity <- mean(masterSpec)
      
      # Store the results including the combination of variables
      temp_results_list[[i]] <- list(variables = index_set, Sensitivity = avg_sensitivity, Specificity = avg_specificity)
    }
    
    end_time <- Sys.time()
    time_taken <- end_time - start_time
    cat("Time taken:", time_taken, "\n")
    
    # Store the results for this iteration
    results_list[[num_vars]] <- temp_results_list
    
    # Get the maximum mean specificity for this number of variables
    max_mean_specificity_current <- max(sapply(temp_results_list, function(x) x$Specificity))
    
    # Check if the maximum mean specificity for the current number of variables is less than the previous maximum
    # if (max_mean_specificity_current < max_mean_specificity_previous) {
    #   cat("Maximum specificity reached for", num_vars, "variables is less than previous maximum. Stopping further iterations.\n")
    #   break
    # }
    
    # Update the maximum mean specificity from previous iterations
    # max_mean_specificity_previous <- max_mean_specificity_current
  }
  
  return(results_list)
}

# Define the list of indexes to loop through
modelIdx <- c(2,4,7,12,15,16,18,19,20,24,29,30,32,33,34,36) #significant features

# Define the maximum number of variables
max_vars <- 15

# Call the function to calculate combinations
results <- calculate_combinations(modelIdx, max_vars)

# Determine the maximum expected number of combinations
max_combinations <- (max_vars - 8) * 10  # Assuming a maximum of 10 combinations per number of variables

# Preallocate the output data frame with maximum expected number of rows
output_df <- data.frame(Number_of_Variables = integer(max_combinations),
                        Variable_Indexes = character(max_combinations),
                        Mean_Sensitivity = numeric(max_combinations),
                        Mean_Specificity = numeric(max_combinations),
                        Sum_of_Sensitivity_and_Specificity = numeric(max_combinations),
                        stringsAsFactors = FALSE)

# Loop over different number of variables
for (num_vars in seq(8, max_vars)) {
  cat("\nTop 10 combinations with the highest specificity for", num_vars, "variables:\n")

  sorted_indices <- order(sapply(results[[num_vars]], function(x) x$Specificity), decreasing = TRUE)
  for (i in 1:min(10, length(sorted_indices))) {
    index <- sorted_indices[i]
    # cat("Combination", i, ": Variables =", results[[num_vars]][[index]]$variables, ", Specificity =", results[[num_vars]][[index]]$Specificity, "\n")

    # Assign the results to the preallocated rows in the output data frame
    row_index <- (num_vars - 8) * 10 + i  # Calculate the row index
    output_df$Number_of_Variables[row_index] <- num_vars
    output_df$Variable_Indexes[row_index] <- paste(results[[num_vars]][[index]]$variables, collapse = ", ")
    output_df$Mean_Sensitivity[row_index] <- results[[num_vars]][[index]]$Sensitivity
    output_df$Mean_Specificity[row_index] <- results[[num_vars]][[index]]$Specificity
    output_df$Sum_of_Sensitivity_and_Specificity[row_index] <- results[[num_vars]][[index]]$Sensitivity + results[[num_vars]][[index]]$Specificity
  }
}

# Print the final output data frame
print(output_df)


From a pool of these variables, Age, BusinessTravel, DistanceFromHome, EnvironmentSatisfaction, JobInvolvement, JobLevel, JobRole, JobSatisfaction, MaritalStatus, MonthlyIncome, OverTime, StockOptionLevel, TotalWorkingYears, WorkLifeBalance, YearsAtCompany, YearsInCurrentRole, YearsWithCurrManager, I try to predict which combinations might yield the highest sensitivity and specificity. Overall, it doesn’t look very promising, perhaps because I didn’t adjust the threshold or tune the parameter k. I choose generally the best performing set of increasing numbers of variables to use in the next block of code, where I will tune the parameters.


Using several of the what seem likely to be the best combinations of explanatory variables, I tune several parameters in the k-NN model. I try to adjust and tune the thresholding, because the dataset is unbalanced with only 16% “Yes” in the Attrition variable. I also tune the number of neighbors, k. I evaluate all combinations of variables and tuning parameters with both external and internal validation. There is probably a better, clearer way to tune k. 

# I comment out some parameters to make a demo version of this code, so that it doesn't take so long to run.

# define parameters
modelIdx_list = list(
  c(2, 4, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 32, 33, 34, 36), # sig numeric vars (16)
  # c(12,16,19,24,29,33,34,36), #8var
  # c(16,18,20,24,29,33,34,36), #8var
  # c(2,12,16,19,24,29,33,34,36), #9var
  # c(2,12,16,19,24,29,30,33,34,36), #10var
  # c(2,12,16,19,20,24,29,30,33,34,36), #11var
  # c(2,7,16,18,19,20,24,29,30,33,34,36), #12var
  # c(2,7,12,16,18,19,20,24,29,30,33,34,36), #13var
  c(2,7,12,15,16,18,19,20,24,29,30,33,34,36), #14var
  # c(2,7,12,15,16,18,19,20,24,29,30,32,33,34,36), #15var
  # c(12,15,16,19,20,24,29,30,32,33,34,36),     # NB Combination 2 (my hand-picked variables) minus job role
  c(4,7,12,15,16,19,20,24,29,30,32,33,34,36)    # NB Combination 4 (the *best*) minus job role
  # c(2, 7, 20, 22, 25, 30, 31, 33, 34, 35, 36) # all numeric variables
)

# actual set of parameters used
# thresholds = seq(0.1, 0.6, 0.02) #classifier thresholds to try for "Yes" based on ~0.16 proportion yes to no
# numKs = seq(1, 49, 2) #odd Ks to try
# iters = 100  #train/test split iterations
# splitPerc = 0.7  #percentage of data for training

# demo set
thresholds = seq(0.1, 0.5, 0.05) #classifier thresholds to try for "Yes" based on ~0.16 proportion yes to no
numKs = seq(3, 49, 2) #odd Ks to try
iters = 10  #train/test split iterations
splitPerc = 0.7  #percentage of data for training

# for debugging
# modelIdx = c(2, 4, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 32, 33, 34, 36)
# threshold = 0.5
# k = 11
# i = 1

# initialize a list to store results
results_list = list()

# time the loop 
loop_start = Sys.time()
cat("Start time:", loop_start, "\n")
Start time: 1713729397 
# loop through modelIdx combinations
for (modelIdx in modelIdx_list) {
  
  # loop through the thresholds
  for (threshold in thresholds) {
    
    # loop through the Ks
    for (k in numKs) {
      
      # time the K loop
      k_start = Sys.time()
      
      # make holders for the stats from each iteration for this modelIdx, threshold and K
      iteration_stats = matrix(nrow = iters, ncol = 5)
      colnames(iteration_stats) = c("Seed", "Threshold", "K", "Sensitivity", "Specificity")
      
      # counter for row index in iteration_stats
      row_counter = 1
      
      # external cross-validation loop
      for (i in 1:iters) {

        set.seed(i)

        # generate the test train split
        trainIdx = sample(1:nrow(numerical_df), round(splitPerc * nrow(numerical_df)))
        AttritionTrn = numerical_df[trainIdx, ]
        AttritionTst = numerical_df[-trainIdx, ]

        # train kNN model with current k and feature (modelIdx) set
        classifications = knn(AttritionTrn[, modelIdx], AttritionTst[, modelIdx], AttritionTrn$Attrition, prob = T, k = k)
        # create a table of predicted vs actual values for assessing classification accuracy
        #table(classifications, AttritionTst$Attrition)
   
        # display the classifications and their attributes; useful for debugging and understanding model output
        classifications
        attributes(classifications)
        
        # compute probabilities specifically for the "YES" class, adjusting based on predicted labels
        probs = ifelse(classifications == "YES", attributes(classifications)$prob, 1 - attributes(classifications)$prob)

        # apply the new threshold to reclassify observations
        NewClass = ifelse(probs >= threshold, "Yes", "No")

        # this didn't work if all the predictions were No because the Yes row was missing 
        # tabulate the new classifications against actual values
        # table(NewClass, AttritionTst$Attrition)
        # calculate the confusion matrix
        # don't need to relevel the confusion matrix because I am looking at sensitivity + specificity
        # CM_no = confusionMatrix(table(relevel(as.factor(NewClass), ref = "No"), AttritionTst$Attrition), mode = "everything")
        
        # create a table with rows for both "Yes" and "No" classes (in the event there are zero "Yes"s)
        table_predicted_actual = matrix(0, nrow = 2, ncol = 2, dimnames = list(c("No", "Yes"), c("No", "Yes")))
        
        # populate the counts based on the predictions and actual classes
        table_predicted_actual["No", "No"] = sum(NewClass == "No" & AttritionTst$Attrition == "No")
        table_predicted_actual["No", "Yes"] = sum(NewClass == "No" & AttritionTst$Attrition == "Yes")
        table_predicted_actual["Yes", "No"] = sum(NewClass == "Yes" & AttritionTst$Attrition == "No")
        table_predicted_actual["Yes", "Yes"] = sum(NewClass == "Yes" & AttritionTst$Attrition == "Yes")

        # calculate the confusion matrix for this iteration
        CM_no = confusionMatrix(table_predicted_actual, mode = "everything")
        
        # get sensitivity and specificity for "No" class
        sens_no = CM_no[4]$byClass["Sensitivity"] # because reference (positive class) is set to no
        spec_no = CM_no[4]$byClass["Specificity"]

        # store results for that iteration
        iteration_stats[row_counter, ] = c(i, threshold, k, sens_no, spec_no)
        row_counter = row_counter + 1

      } # complete external cross-validation loop
      
      # initialize variables to store predictions and actual values to calculate confusion matrix after all LOO
      all_predictions = c()
      all_actual = c()
      
      # internal cross-validation (Leave-One-Out Cross-Validation)
      classifications = knn.cv(numerical_df[, modelIdx], numerical_df$Attrition,
                         prob = TRUE, k = k)
      # create a table of predicted vs actual values for assessing classification accuracy
      #table(classifications, AttritionTst$Attrition)
   
      # display the classifications and their attributes; useful for debugging and understanding model output
      classifications
      attributes(classifications)
        
      # compute probabilities specifically for the "YES" class, adjusting based on predicted labels
      probs = ifelse(classifications == "YES", attributes(classifications)$prob, 1 - attributes(classifications)$prob)

      # apply the new threshold to reclassify observations
      NewClass = ifelse(probs >= threshold, "Yes", "No")
      
      # tabulate the new classifications against actual values
      # table(NewClass, AttritionTst$Attrition)
      # calculate the confusion matrix
      # don't need to relevel the confusion matrix because I am looking about sensitivity + specificity
      # CM_no = confusionMatrix(table(relevel(as.factor(NewClass), ref = "No"), cs2_conv$Attrition), mode = "everything")
      
      # create a table with rows for both "Yes" and "No" classes (in the event there are zero "Yes"s)
      table_predicted_actual = matrix(0, nrow = 2, ncol = 2, dimnames = list(c("No", "Yes"), c("No", "Yes")))
        
      # populate the counts based on the predictions and actual classes
      table_predicted_actual["No", "No"] = sum(NewClass == "No" & cs2_conv$Attrition == "No")
      table_predicted_actual["No", "Yes"] = sum(NewClass == "No" & cs2_conv$Attrition == "Yes")
      table_predicted_actual["Yes", "No"] = sum(NewClass == "Yes" & cs2_conv$Attrition == "No")
      table_predicted_actual["Yes", "Yes"] = sum(NewClass == "Yes" & cs2_conv$Attrition == "Yes")
        
      # calculate the confusion matrix for this iteration
      CM_no = confusionMatrix(table_predicted_actual, mode = "everything")
        
      # get sensitivity and specificity for "No" class
      sens_icv = CM_no[4]$byClass["Sensitivity"] # because reference (positive class) is set to no
      spec_icv = CM_no[4]$byClass["Specificity"]

      # calculate mean sensitivity and specificity over ECV and ICV for this combination of modelIdx, threshold and k
      # not sure if I should even average these??
      avg_sens = mean(c(mean(iteration_stats[, "Sensitivity"]), sens_icv))
      avg_spec = mean(c(mean(iteration_stats[, "Specificity"]), spec_icv))
      
      # store results for this combination of modelIdx, threshold and K
      results_list = c(results_list, list(
        data.frame(
          ModelIdx = toString(modelIdx),
          Threshold = threshold,
          K = k,
          AvgSensitivity = avg_sens,
          AvgSpecificity = avg_spec,
          AvgSum = avg_sens + avg_spec
        )
      ))

        # time the k loop
        k_end = Sys.time()
        time_taken_thresh = difftime(k_end, k_start, units = "secs")
        # cat("K Loop Time:", time_taken_thresh, "secs \n")
        # cat("ModelIdx:", toString(modelIdx), "- Threshold:", threshold, "- K:", k, "\n")
      
    } # complete k loop

  } # complete threshold loop
  
  # print progress report
  progress_time = Sys.time()
  progress = difftime(progress_time, loop_start, units = "mins")
  cat("Total Elapsed Time:", progress, "mins \n")
  
} # complete modelIdx loop
Total Elapsed Time: 0.4169225 mins 
Total Elapsed Time: 0.7708993 mins 
Total Elapsed Time: 1.122256 mins 
# loop time
# loop_end = Sys.time()
# time_taken_loop = difftime(loop_end, loop_start, units = "mins")
# cat("Total Loop Time:", time_taken_loop, "mins \n")

# convert results_list to a data frame
results_df = do.call(rbind, results_list)

# plot the optimal k (though not particularly helpful or needed with the other tuning)
# aggregate results by K
results_agg = results_df %>%
  group_by(K) %>%
  dplyr::summarize(Mean_Sensitivity = mean(AvgSensitivity),
            Mean_Specificity = mean(AvgSpecificity))
# plot the average sensitivity and specificity for each K
ggplot(results_agg, aes(x = K)) +
  geom_line(aes(y = Mean_Sensitivity, color = "Mean Sensitivity")) +
  geom_line(aes(y = Mean_Specificity, color = "Mean Specificity")) +
  labs(title = "Mean sensitivity and specificity for different values of K",
       x = "K parameter", y = "Metric", color = "Metric") +
  scale_color_manual(values = c("Mean Sensitivity" = "darkgreen", "Mean Specificity" = "darkblue")) +
  theme_bw()

# output top 10 combinations for each ModelIdx
top_10_combos = results_df %>%
  arrange(ModelIdx, desc(AvgSum), desc(AvgSpecificity), desc(AvgSensitivity)) %>%
  group_by(ModelIdx) %>%
  top_n(10, wt = AvgSum)
kable(top_10_combos, caption = "demo top 10 sensitivity + specificity tuned knn parameters") %>% kable_styling(full_width = FALSE, position = "left")
demo top 10 sensitivity + specificity tuned knn parameters
ModelIdx Threshold K AvgSensitivity AvgSpecificity AvgSum
2, 4, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 41 0.8368230 0.6553327 1.492156
2, 4, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 43 0.8195869 0.6709875 1.490574
2, 4, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 39 0.7915156 0.6956844 1.487200
2, 4, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 49 0.8248028 0.6613105 1.486113
2, 4, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 45 0.8019084 0.6836708 1.485579
2, 4, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 47 0.8388773 0.6412330 1.480110
2, 4, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 37 0.8068725 0.6692766 1.476149
2, 4, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 33 0.7747236 0.6965216 1.471245
2, 4, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 35 0.8256930 0.6421069 1.467800
2, 4, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.10 43 0.6672257 0.7987358 1.465962
2, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 33, 34, 36 0.15 41 0.8100142 0.6421706 1.452185
2, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 33, 34, 36 0.15 43 0.7889211 0.6613497 1.450271
2, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 33, 34, 36 0.15 29 0.7937247 0.6544004 1.448125
2, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 33, 34, 36 0.15 27 0.8173574 0.6294154 1.446773
2, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 33, 34, 36 0.15 47 0.8091314 0.6371005 1.446232
2, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 33, 34, 36 0.20 49 0.8734955 0.5707366 1.444232
2, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 33, 34, 36 0.15 31 0.7705838 0.6735651 1.444149
2, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 33, 34, 36 0.20 43 0.8764539 0.5676696 1.444123
2, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 33, 34, 36 0.20 39 0.8709846 0.5730479 1.444033
2, 7, 12, 15, 16, 18, 19, 20, 24, 29, 30, 33, 34, 36 0.20 33 0.8676089 0.5762523 1.443861
4, 7, 12, 15, 16, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 33 0.7583289 0.7413052 1.499634
4, 7, 12, 15, 16, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 49 0.8057511 0.6937896 1.499541
4, 7, 12, 15, 16, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 39 0.7694411 0.7289421 1.498383
4, 7, 12, 15, 16, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 47 0.8191319 0.6781339 1.497266
4, 7, 12, 15, 16, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 45 0.7807184 0.7157678 1.496486
4, 7, 12, 15, 16, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 43 0.7962160 0.7000963 1.496312
4, 7, 12, 15, 16, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 37 0.7892095 0.7068075 1.496017
4, 7, 12, 15, 16, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 31 0.7746572 0.7148029 1.489460
4, 7, 12, 15, 16, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 35 0.8105285 0.6769495 1.487478
4, 7, 12, 15, 16, 19, 20, 24, 29, 30, 32, 33, 34, 36 0.15 41 0.8100356 0.6700381 1.480074


Based on this parameter tuning, the highest sum of sensitivity and specificity scores my k-NN model achieves is 148.78 (Sensitivity of 75.16% and Specificity of 73.62%). The optimization was achieved with ModelIdx = c(4, 7, 12, 15, 16, 19, 20, 24, 29, 30, 32, 33, 34, 36), which are the indexes of the columns in cs2 (and numerical_df) and k = 41 and threshold (of "Yes" >=) = 0.14. This is the same list of variables that achieve the best performance (148.79) in the Naive Bayes model, minus JobRole. Sensitivity and specificity are more balanced in this model, probably because the threshold here is quite low, 0.14 versus 0.46 in the Naive Bayes model. I think I will use the Naive Bayes model for the final predictions because it has a tiny bit higher sum of sensitivity and specificity (only 0.01), without using what seems like a very low threshold 0.14, when the percentage of Attrition in the actual data set is ~16%. I would prefer to use the simpler model. While the Naive Bayes model does use one more variable, I think the work of pre-processing variables for k-NN offsets the extra variable.


Objective 4: Build a R Shiny app to visualize some of the relationships.


This R Shiny app displays the distributions of monthly income by attrition group in a boxplot and histograms. A user can select individual or combinations of job roles and also a salary range. The app will interactively update with the distributions for the user selections and will display the percent of selected employees in each attrition group.

R Shiny Employee Attrition and Income App is here: https://kdhenderson.shinyapps.io/Employee_Attrition_and_Income/.

Objective 5: Predict the attrition on the competition set.


I import the unlabeled competition data set from the cloud as competition. I convert the numerical ranked variables to factors. So that my column indexes are the same as those in the primary data set, I add an Attrition column. I train a Naive Bayes model on the entire labeled primary data set using the tuned alpha parameter. Then I adjust the classifications with the tuned threshold. 

# make predictions with Naive Bayes model

# variables used: `BusinessTravel`, `DistanceFromHome`, `EnvironmentSatisfaction`, `JobInvolvement`, `JobLevel`, `JobRole`, `MaritalStatus`, `MonthlyIncome`, `OverTime`, `StockOptionLevel`, `TotalWorkingYears`, `WorkLifeBalance`, `YearsAtCompany`, `YearsInCurrentRole`, `YearsWithCurrManager`

# parameters
# train_dataframe = cs2_conv
# adjust index numbers based on missing Attrition column #3 or add column to competition set
ModelIdx = c(4, 7, 12, 15, 16, 17, 19, 20, 24, 29, 30, 32, 33, 34, 36)
alpha = 0.7
threshold = 0.46 # "Yes" >=

# import data: CaseStudy2CompSet No Attrition.csv from AWS S3 msdsds6306 bucket

url = "https://msdsds6306.s3.us-east-2.amazonaws.com/CaseStudy2CompSet+No+Attrition.csv"
# encoded_url = URLencode(url) # need to encode the spaces as %20 (or do it manually)
competition = read.table(textConnection(getURL(url)), sep = ",", header = TRUE, stringsAsFactors = TRUE)

# save a copy of the competition unlabeled data
# write.csv(competition, file = "data/CaseStudy2CompSet No Attrition.csv", row.names = FALSE)

# get a sense of the data
str(competition)
'data.frame':   300 obs. of  35 variables:
 $ ID                      : int  1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 ...
 $ Age                     : int  35 33 26 55 29 51 52 39 31 31 ...
 $ BusinessTravel          : Factor w/ 3 levels "Non-Travel","Travel_Frequently",..: 3 3 3 3 3 2 1 3 3 2 ...
 $ DailyRate               : int  750 147 1330 1311 1246 1456 585 1387 1062 534 ...
 $ Department              : Factor w/ 3 levels "Human Resources",..: 2 1 2 2 3 2 3 2 2 2 ...
 $ DistanceFromHome        : int  28 2 21 2 19 1 29 10 24 20 ...
 $ Education               : int  3 3 3 3 3 4 4 5 3 3 ...
 $ EducationField          : Factor w/ 6 levels "Human Resources",..: 2 1 4 2 2 4 2 4 4 2 ...
 $ EmployeeCount           : int  1 1 1 1 1 1 1 1 1 1 ...
 $ EmployeeNumber          : int  1596 1207 1107 505 1497 145 2019 1618 1252 587 ...
 $ EnvironmentSatisfaction : int  2 2 1 3 3 1 1 2 3 1 ...
 $ Gender                  : Factor w/ 2 levels "Female","Male": 2 2 2 1 2 1 2 2 1 2 ...
 $ HourlyRate              : int  46 99 37 97 77 30 40 76 96 66 ...
 $ JobInvolvement          : int  4 3 3 3 2 2 3 3 2 3 ...
 $ JobLevel                : int  2 1 1 4 2 3 1 2 2 3 ...
 $ JobRole                 : Factor w/ 9 levels "Healthcare Representative",..: 3 2 3 4 8 1 9 5 1 1 ...
 $ JobSatisfaction         : int  3 3 3 4 3 1 4 1 1 3 ...
 $ MaritalStatus           : Factor w/ 3 levels "Divorced","Married",..: 2 2 1 3 1 3 1 2 3 2 ...
 $ MonthlyIncome           : int  3407 3600 2377 16659 8620 7484 3482 5377 6812 9824 ...
 $ MonthlyRate             : int  25348 8429 19373 23258 23757 25796 19788 3835 17198 22908 ...
 $ NumCompaniesWorked      : int  1 1 1 2 1 3 2 2 1 3 ...
 $ Over18                  : Factor w/ 1 level "Y": 1 1 1 1 1 1 1 1 1 1 ...
 $ OverTime                : Factor w/ 2 levels "No","Yes": 1 1 1 2 1 1 1 1 1 1 ...
 $ PercentSalaryHike       : int  17 13 20 13 14 20 15 13 19 12 ...
 $ PerformanceRating       : int  3 3 4 3 3 4 3 3 3 3 ...
 $ RelationshipSatisfaction: int  4 4 3 3 3 3 2 4 2 1 ...
 $ StandardHours           : int  80 80 80 80 80 80 80 80 80 80 ...
 $ StockOptionLevel        : int  2 1 1 0 2 0 2 3 0 0 ...
 $ TotalWorkingYears       : int  10 5 1 30 10 23 16 10 10 12 ...
 $ TrainingTimesLastYear   : int  3 2 0 2 3 1 3 3 2 2 ...
 $ WorkLifeBalance         : int  2 3 2 3 3 2 2 3 3 3 ...
 $ YearsAtCompany          : int  10 5 1 5 10 13 9 7 10 1 ...
 $ YearsInCurrentRole      : int  9 4 1 4 7 12 8 7 9 0 ...
 $ YearsSinceLastPromotion : int  6 1 0 1 0 12 0 7 1 0 ...
 $ YearsWithCurrManager    : int  8 4 0 2 4 8 0 7 8 0 ...
summary(competition)
       ID            Age                  BusinessTravel   DailyRate     
 Min.   :1171   Min.   :19.00   Non-Travel       : 32    Min.   : 102.0  
 1st Qu.:1246   1st Qu.:31.00   Travel_Frequently: 57    1st Qu.: 448.0  
 Median :1320   Median :36.00   Travel_Rarely    :211    Median : 775.0  
 Mean   :1320   Mean   :37.86                            Mean   : 784.8  
 3rd Qu.:1395   3rd Qu.:44.00                            3rd Qu.:1117.0  
 Max.   :1470   Max.   :60.00                            Max.   :1490.0  
                                                                         
                  Department  DistanceFromHome   Education    
 Human Resources       : 11   Min.   : 1.00    Min.   :1.000  
 Research & Development:209   1st Qu.: 2.00    1st Qu.:2.000  
 Sales                 : 80   Median : 7.00    Median :3.000  
                              Mean   : 9.26    Mean   :2.973  
                              3rd Qu.:14.00    3rd Qu.:4.000  
                              Max.   :29.00    Max.   :5.000  
                                                              
          EducationField EmployeeCount EmployeeNumber   EnvironmentSatisfaction
 Human Resources :  7    Min.   :1     Min.   :   2.0   Min.   :1.000          
 Life Sciences   :130    1st Qu.:1     1st Qu.: 508.8   1st Qu.:2.000          
 Marketing       : 27    Median :1     Median : 994.5   Median :3.000          
 Medical         : 94    Mean   :1     Mean   :1020.9   Mean   :2.733          
 Other           : 12    3rd Qu.:1     3rd Qu.:1542.5   3rd Qu.:4.000          
 Technical Degree: 30    Max.   :1     Max.   :2065.0   Max.   :4.000          
                                                                               
    Gender      HourlyRate     JobInvolvement     JobLevel  
 Female:105   Min.   : 30.00   Min.   :1.000   Min.   :1.0  
 Male  :195   1st Qu.: 50.00   1st Qu.:2.000   1st Qu.:1.0  
              Median : 66.00   Median :3.000   Median :2.0  
              Mean   : 66.07   Mean   :2.743   Mean   :2.2  
              3rd Qu.: 83.00   3rd Qu.:3.000   3rd Qu.:3.0  
              Max.   :100.00   Max.   :4.000   Max.   :5.0  
                                                            
                      JobRole   JobSatisfaction  MaritalStatus MonthlyIncome  
 Research Scientist       :61   Min.   :1.000   Divorced: 65   Min.   : 1232  
 Sales Executive          :57   1st Qu.:2.000   Married :128   1st Qu.: 3034  
 Laboratory Technician    :55   Median :3.000   Single  :107   Median : 5208  
 Manufacturing Director   :31   Mean   :2.767                  Mean   : 7103  
 Manager                  :30   3rd Qu.:4.000                  3rd Qu.: 9750  
 Healthcare Representative:29   Max.   :4.000                  Max.   :19973  
 (Other)                  :37                                                 
  MonthlyRate    NumCompaniesWorked Over18  OverTime  PercentSalaryHike
 Min.   : 2097   Min.   :0.000      Y:300   No :212   Min.   :11.00    
 1st Qu.: 8420   1st Qu.:1.000              Yes: 88   1st Qu.:12.00    
 Median :15091   Median :2.000                        Median :14.00    
 Mean   :14499   Mean   :2.547                        Mean   :15.17    
 3rd Qu.:20330   3rd Qu.:4.000                        3rd Qu.:18.00    
 Max.   :26914   Max.   :9.000                        Max.   :25.00    
                                                                       
 PerformanceRating RelationshipSatisfaction StandardHours StockOptionLevel
 Min.   :3.000     Min.   :1.000            Min.   :80    Min.   :0.0000  
 1st Qu.:3.000     1st Qu.:2.000            1st Qu.:80    1st Qu.:0.0000  
 Median :3.000     Median :3.000            Median :80    Median :1.0000  
 Mean   :3.153     Mean   :2.803            Mean   :80    Mean   :0.7833  
 3rd Qu.:3.000     3rd Qu.:4.000            3rd Qu.:80    3rd Qu.:1.0000  
 Max.   :4.000     Max.   :4.000            Max.   :80    Max.   :3.0000  
                                                                          
 TotalWorkingYears TrainingTimesLastYear WorkLifeBalance YearsAtCompany  
 Min.   : 0.00     Min.   :0.000         Min.   :1.000   Min.   : 0.000  
 1st Qu.: 6.00     1st Qu.:2.000         1st Qu.:2.000   1st Qu.: 3.000  
 Median :10.00     Median :2.000         Median :3.000   Median : 5.000  
 Mean   :12.44     Mean   :2.683         Mean   :2.747   Mean   : 7.527  
 3rd Qu.:18.00     3rd Qu.:3.000         3rd Qu.:3.000   3rd Qu.:10.000  
 Max.   :38.00     Max.   :6.000         Max.   :4.000   Max.   :37.000  
                                                                         
 YearsInCurrentRole YearsSinceLastPromotion YearsWithCurrManager
 Min.   : 0.00      Min.   : 0.00           Min.   : 0.00       
 1st Qu.: 2.00      1st Qu.: 0.00           1st Qu.: 2.00       
 Median : 3.00      Median : 1.00           Median : 3.00       
 Mean   : 4.33      Mean   : 2.29           Mean   : 4.38       
 3rd Qu.: 7.00      3rd Qu.: 3.00           3rd Qu.: 7.00       
 Max.   :18.00      Max.   :15.00           Max.   :17.00       
                                                                
# convert numerical ranked variables to factors
numVars_to_fact = c("Education", "EnvironmentSatisfaction",
                    "JobInvolvement", "JobLevel", "JobSatisfaction",
                    "PerformanceRating", "RelationshipSatisfaction",
                    "StockOptionLevel", "WorkLifeBalance")
competition = competition %>%
  mutate(across(all_of(numVars_to_fact), as.factor))
# check the conversion
# str(competition)

# add the Attrition column between Age and BusinessTravel
competition = competition %>%
  mutate(Attrition = NA, .after = "Age")
# str(competition)

# train the Naive Bayes model
fullsetNBmodel = naiveBayes(cs2_conv[, modelIdx], cs2_conv$Attrition, laplace = alpha)

# predict the labels on the competition set
preds = predict(fullsetNBmodel, competition[, modelIdx], type = "raw") # raw returns the probabilities

# get the Yes probabilities to adjust threshold
attrition_probs = preds[, "Yes"]

# classify with new threshold
predictions = ifelse(attrition_probs >= threshold, "Yes", "No")

# add the labels to the Attrition column
competition = competition %>% mutate(Attrition = factor(predictions))
# str(competition)

# get the proportion of attrition for curiousity
summary(competition$Attrition)
 No Yes 
242  58 
NoAttProb = summary(competition$Attrition)["No"] / sum(summary(competition$Attrition))
NoAttProb
       No 
0.8066667 
AttProb = summary(competition$Attrition)["Yes"] / sum(summary(competition$Attrition))
AttProb
      Yes 
0.1933333 
# make dataframe with just competition set ordered IDs and labels
competitionLabels = competition %>% select(ID, Attrition)
str(competitionLabels)
'data.frame':   300 obs. of  2 variables:
 $ ID       : int  1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 ...
 $ Attrition: Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...
# save to file
# write.csv(competitionLabels, file = "data/Case2PredictionsHenderson Attrition.csv", row.names = FALSE)



Objective 6: Create a linear regression model to predict monthly salaries.

(with < $3000 RMSE for training and validation set)

To create a new dataframe cs2_regres, I transform the original data set by reordering and converting factor variables to integers. Based on the EDA scatter plots, I also derive some quadratic variables. 

# starting with the original dataset `cs2` since the ordinal categorical variables are in an integer class
# there are a few other variables that I could transform into ranked variables, like business travel
# not sure it is valid to do it for marital status or overtime

# make a copy of the original dataset
numerical_df = cs2

# check the data
head(numerical_df$BusinessTravel)
[1] Travel_Rarely     Travel_Rarely     Travel_Frequently Travel_Rarely    
[5] Travel_Frequently Travel_Frequently
Levels: Non-Travel Travel_Frequently Travel_Rarely
# reorder factor levels
numerical_df$BusinessTravel = factor(numerical_df$BusinessTravel, levels = c("Non-Travel", "Travel_Rarely", "Travel_Frequently"), labels = c("Non-Travel", "Travel_Rarely", "Travel_Frequently"))

# rename the levels to numbers
levels(numerical_df$BusinessTravel) = c(1:3)

# convert factor to integer
numerical_df$BusinessTravel = as.integer(numerical_df$BusinessTravel)

# check the conversion
head(numerical_df$BusinessTravel)
[1] 2 2 3 2 3 3
# repeat for marital status and overtime and attrition :/
head(numerical_df$MaritalStatus)
[1] Divorced Single   Single   Married  Single   Divorced
Levels: Divorced Married Single
numerical_df$MaritalStatus = factor(numerical_df$MaritalStatus, levels = c("Single", "Married", "Divorced"), labels = c("Single", "Married", "Divorced"))
levels(numerical_df$MaritalStatus) = c(1:3)
numerical_df$MaritalStatus = as.integer(numerical_df$MaritalStatus)
head(numerical_df$MaritalStatus)
[1] 3 1 1 2 1 3
head(numerical_df$OverTime)
[1] No  No  No  No  Yes No 
Levels: No Yes
numerical_df$OverTime = factor(numerical_df$OverTime, levels = c("Yes", "No"), labels = c("Yes", "No"))
levels(numerical_df$OverTime) = c(1:2)
numerical_df$OverTime = as.integer(numerical_df$OverTime)
head(numerical_df$OverTime)
[1] 2 2 2 2 1 2
head(numerical_df$Attrition)
[1] No No No No No No
Levels: No Yes
numerical_df$Attrition = factor(numerical_df$Attrition, levels = c("Yes", "No"), labels = c("Yes", "No"))
levels(numerical_df$Attrition) = c(1:2)
numerical_df$Attrition = as.integer(numerical_df$Attrition)
head(numerical_df$Attrition)
[1] 2 2 2 2 2 2
# make a new DF, transform x variable (squaring term) and add it as a new column
cs2_regres = numerical_df %>%
  mutate(
    YearsInCurrentRole2 = YearsInCurrentRole^2,
    YearsWithCurrManager2 = YearsWithCurrManager^2)

#indexes from cs2_regres dataframe
ModelIdx = c(2,3,4,5,7,8,12,14,15,16,18,19,21,22,24,25,26,27,29,30,31,32,33,34,35,36,37,38)



To find the variables that produce a model with the lowest RMSE, I start with an empty model formula. In a loop, I add each of the variables in the cs2_regres dataframe independently to build a regression model. I evaluate each model with leave-one-out cross validation. I store each result in a dataframe, sorted by lowest RMSE. Using these values as a guide, I manually choose the variable which performs best. I add it as an explanatory variable to the model and repeat the process with the remaining variables until I can no longer achieve a lower RMSE with additional variables. 

# unused indexes from cs2_regres dataframe 
ModelIdx = c(2,3,4,5,8,14,18,19,21,22,24,25,26,27,29,31,32,33,34,35,37)
  
# initialize an empty dataframe to store results
results = data.frame(Index = numeric(length(ModelIdx)), Variable = character(length(ModelIdx)), RMSE = numeric(length(ModelIdx)))

# get number of rows in data frame
n = nrow(cs2_regres)

# loop through each explanatory variable separately
for (i in seq_along(ModelIdx)) {
  
  # create formula with the current explanatory variable 
  model_formula = as.formula(paste("MonthlyIncome ~ JobLevel + TotalWorkingYears + YearsWithCurrManager + YearsWithCurrManager2 + DistanceFromHome + JobInvolvement + EnvironmentSatisfaction + ", names(cs2_regres)[ModelIdx[i]]))
  # indexes of variables used in model c(16,30,36,7,15,38,12)

  # initialize vector to store squared error from each leave-one-out loop
  cv_error_model = numeric(n)
  
  # loop through setting each row as test set for internal n-fold CV
  for (j in 1:n) {
    # leave out the j-th observation
    test_row = cs2_regres[j, ]
    
    # use the remaining data for training       
    train_data = cs2_regres[-j, ]
    
    # fit the model with train_data
    model = lm(model_formula, data = train_data)
    
    # predict on the left-out observation
    pred = predict(model, newdata = test_row)
    
    # calculate the squared error
    cv_error_model[j] = (test_row$MonthlyIncome - pred)^2
  }
  
  # calculate the root mean squared error (RMSE) for the current model
  RMSE = sqrt(mean(cv_error_model))
  
  # store the variable index, name, and RMSE in the results dataframe
  results[i, "Index"] = ModelIdx[i]
  results[i, "Variable"] = names(cs2_regres)[ModelIdx[i]]
  results[i, "RMSE"] = RMSE
}

# sort results by RMSE in ascending order
results = results[order(results$RMSE), ]

# print the sorted table
kable(results, caption = "demo of resulting RSME for each 1 added variable") %>% kable_styling(full_width = FALSE, position = "left")
demo of resulting RSME for each 1 added variable
Index Variable RMSE
12 25 PercentSalaryHike 1376.463
9 21 MonthlyRate 1376.495
1 2 Age 1376.499
16 31 TrainingTimesLastYear 1376.594
13 26 PerformanceRating 1376.663
6 14 HourlyRate 1376.674
17 32 WorkLifeBalance 1376.718
3 4 BusinessTravel 1376.755
2 3 Attrition 1376.770
10 22 NumCompaniesWorked 1376.825
8 19 MaritalStatus 1376.835
15 29 StockOptionLevel 1376.843
11 24 OverTime 1376.953
14 27 RelationshipSatisfaction 1376.964
7 18 JobSatisfaction 1376.974
5 8 Education 1377.005
4 5 DailyRate 1377.028
20 35 YearsSinceLastPromotion 1377.295
19 34 YearsInCurrentRole 1377.296
21 37 YearsInCurrentRole2 1377.509
18 33 YearsAtCompany 1377.707


Measured with internal n-fold cross validation, I achieve the lowest RMSE of 1375.36 with the following explanatory variables JobLevel, TotalWorkingYears, YearsWithCurrManager, YearsWithCurrManager2, DistanceFromHome, JobInvolvement, EnvironmentSatisfaction.


To measure separate RMSEs for a training and a validation set, I use external cross validation for a linear regression model of MonthlyIncome using the variables above. 

# model formula from variable indexes (16,30,36,7,15,38,12)
model_formula = as.formula("MonthlyIncome ~ JobLevel + TotalWorkingYears + YearsWithCurrManager + YearsWithCurrManager2 + DistanceFromHome + JobInvolvement + EnvironmentSatisfaction")

# number of train/test splits
iters = 100

# split percentage
split_perc = 0.7

# initialize vector to store squared error from each train/test split loop for training and validation sets
cv_error_train = numeric(iters)
cv_error_test = numeric(iters)
  
# external cross-validation loop
for (i in 1:iters) {
  
  set.seed(i)

  # generate the test train split
  trainIdx = sample(1:nrow(cs2_regres), round(splitPerc * nrow(cs2_regres)))
  IncomeTrn = cs2_regres[trainIdx, ]
  IncomeTst = cs2_regres[-trainIdx, ]
    
  # fit the model with train_data
  model = lm(model_formula, data = IncomeTrn)
    
  # predict on the training set (same data used to make model)
  predTrn = predict(model, newdata = IncomeTrn)
  
  # calculate the mean squared error of training pred
  cv_error_train[i] = mean((IncomeTrn$MonthlyIncome - predTrn)^2)
  
  # predict on the training set (same data used to make model)
  predTst = predict(model, newdata = IncomeTst)
    
  # calculate the mean squared error of training pred
  cv_error_test[i] = mean((IncomeTst$MonthlyIncome - predTst)^2)
}
  
# calculate the root mean squared error (RMSE) for the training set
RMSE_trn = sqrt(mean(cv_error_train)) # root of avg of error from each iteration 
  
# calculate the root mean squared error (RMSE) for the validation set
RMSE_tst = sqrt(mean(cv_error_test))
  
# print the results
cat("\nRMSE of training set: ", RMSE_trn, "\n")

RMSE of training set:  1357.371 
cat("\nRMSE of validation set: ", RMSE_tst, "\n")

RMSE of validation set:  1381.737


For my linear regression model, the RMSE of my training set and validation sets are 1357.37 and 1381.74, respectively. To achieve this, I used these variables, JobLevel, TotalWorkingYears, YearsWithCurrManager, YearsWithCurrManager2, DistanceFromHome, JobInvolvement, EnvironmentSatisfaction. This list includes YearsWithCurrManager2, which is a variable I derived from squaring YearsWithCurrManager.


I import the unlabeled competition data set from the cloud as competition. I create two new variables by squaring existing variables. So that my column indexes are the same as those in the primary data set, I add an MonthlyIncome column. I train a Linear Regression model using the optimized variables and all the observations in the labeled primary data set. 

# make predictions with linear regression model

# variables used: `JobLevel`, `TotalWorkingYears`, `YearsWithCurrManager`, `YearsWithCurrManager2`, `DistanceFromHome`, `JobInvolvement`, `EnvironmentSatisfaction`

# parameters
# train_dataframe = cs2_regres
# adjust index numbers based on missing MonthlyIncome column or add column to competition set
# regresIdx = c(16,30,36,7,15,38,12)


# import data: CaseStudy2CompSet No Salary.csv from AWS S3 msdsds6306 bucket

# first column header is `ï..ID` instead of `ID` which I guess is a UTF-8 encoding issue 
# url = "https://msdsds6306.s3.us-east-2.amazonaws.com/CaseStudy2CompSet+No+Salary.csv"
# competition = read.table(textConnection(getURL(url)), sep = ",", header = TRUE, stringsAsFactors = TRUE)

# so I use read.csv and specify encoding = "UTF-8" and it imports correctly.
url = "https://msdsds6306.s3.us-east-2.amazonaws.com/CaseStudy2CompSet+No+Salary.csv"
competition = read.csv(url, header = TRUE, stringsAsFactors = TRUE, encoding = "UTF-8")

# save a copy of the competition unlabeled data
# write.csv(competition, file = "data/CaseStudy2CompSet No Salary.csv", row.names = FALSE)

# get a sense of the data
# str(competition)
# summary(competition)

# create squared variables, both to keep the indexes consistent
competition = competition %>%
  mutate(
    YearsInCurrentRole2 = YearsInCurrentRole^2,
    YearsWithCurrManager2 = YearsWithCurrManager^2)
# check the conversion
# str(competition)

# add the MonthlyIncome column between MaritalStatus and MonthlyRate 
competition = competition %>%
  mutate(MonthlyIncome = NA, .after = "MaritalStatus")
# str(competition)

# train the linear regression model on the full `cs2_regres` data set
fullset_LM_model = lm(model_formula, data = cs2_regres)

# predict the labels on the competition set
preds = predict(fullset_LM_model, competition)

# add the labels to the MonthlyIncome column
competition = competition %>% mutate(MonthlyIncome = as.integer(preds))
# str(competition)

# for curiousity get the summary of MonthlyIncome from both datasets
summary(cs2_regres$MonthlyIncome)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   1081    2840    4946    6390    8182   19999 
summary(competition$MonthlyIncome)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   1576    2340    6008    6242    7056   19117 
# make dataframe with just competition set ordered IDs and labels
competitionLabels = competition %>% select(ID, MonthlyIncome)
# str(competitionLabels)

# save to file
# write.csv(competitionLabels, file = "data/Case2PredictionsHenderson Salary.csv", row.names = FALSE)



Conclusion


The goal of this analysis is to identify factors that lead to and help predict employee attrition for the CEO and CFO of Frito Lay. This analysis includes 36 unique features from 870 employees. Using a combination of visualizations and statistical techniques, I identify monthly income, job level and over time work as top factors leading to employee attrition. I also document trends across different job roles and provide a tool for interactive visualization of trends in income and attrition rates among these roles. I constructed a model to forecast employee attrition by identifying variables and parameters that yielded the lowest error rates. I also developed an optimized linear regression model for forecasting monthly salaries. With these models, I offer predictions for 300 employees whose attrition outcomes are uncertain and a separate cohort whose salaries are undetermined. Importantly, these data reveal targeted steps that may be taken to mitigate attrition. Specifically, increase monthly income for lower income earners in job level 4, reduce over time work across job levels 1, 2, 3 and 5, prioritize salary hikes and career advancement for personnel in job level 1, where attrition rates are most pronounced. In providing actionable intelligence alongside practical tools, my aim is to empower Frito Lay in cultivating a work environment that promotes the retention and development of high-value talent.

Appendix


R and package versions used 

devtools::session_info()
─ Session info ───────────────────────────────────────────────────────────────
 setting  value
 version  R version 4.3.2 (2023-10-31)
 os       macOS Monterey 12.7.1
 system   x86_64, darwin20
 ui       X11
 language (EN)
 collate  en_US.UTF-8
 ctype    en_US.UTF-8
 tz       America/New_York
 date     2024-04-21
 pandoc   3.1.1 @ /Applications/RStudio.app/Contents/Resources/app/quarto/bin/tools/ (via rmarkdown)

─ Packages ───────────────────────────────────────────────────────────────────
 package      * version    date (UTC) lib source
 backports      1.4.1      2021-12-13 [1] CRAN (R 4.3.0)
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 bslib          0.6.1      2023-11-28 [1] CRAN (R 4.3.0)
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 [1] /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/library

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